Solved: An archer shoots an arrow horizontally at a target

Predict/Explain As you walk briskly down the street, you toss a small ball into the air. (a) If you want the ball to land in your hand when it comes back down, should you toss the ball straight upward, in a forward direction, or in a backward direction, relative to your body?

Asailboat runs before the wind with a constant speed of 4.2 m/s in a direction 32 north of west. How far (a) west and (b) north has the sailboat traveled in 25 min?

As you walk to class with a constant speed of 1.75 m/s, you are moving in a direction that is 18.0 north of east. How much time does it take to change your displacement by (a)20.0 m east or (b) 30.0 m north?

Starting from rest, a car accelerates at up a hill that is inclined 5.5 above the horizontal. How far (a) horizontally and (b) vertically has the car traveled in 12 s?

A particle passes through the origin with a velocity of . If the particles acceleration is , (a) what are its x and y positions after 5.0 s? (b) What are and at this time? (c)Does the speed of this particle increase with time, decrease with time, or increase and then decrease? Explain.

An electron in a cathode-ray tube is traveling horizontally at when deection plates give it an upward acceleration of . (a)How long does it take for the electron to cover a horizontal distance of 6.20 cm? (b) What is its vertical displacement during this time?

Two canoeists start paddling at the same time and head toward a small island in a lake, as shown in Figure 412. Canoeist 1 paddles with a speed of 1.35 m/s at an angle of 45 north of east. Canoeist 2 starts on the opposite shore of the lake, a distance of 1.5 km due east of canoeist 1. (a) In what direction relative to north must canoeist 2 paddle to reach the island? (b)What speed must canoeist 2have if the two canoes are to arrive at the island at the same time?

Predict/Explain Two divers run horizontally off the edge of a low cliff. Diver 2 runs with twice the speed of diver 1. (a)When the divers hit the water, is the horizontal distance covered by diver 2 twice as much, four times as much, or equal to the horizontal distance covered by diver 1? (b) Choose the best explanation from among the following: I. The drop time is the same for both divers. II. Drop distance depends on t2. III. All divers in free fall cover the same distance.

Predict/Explain Two youngsters dive off an overhang into a lake. Diver 1 drops straight down, and diver 2 runs off the cliff with an initial horizontal speed . (a) Is the splashdown speed of diver 2 greater than, less than, or equal to the splashdown speed of diver 1? (b) Choose the best explanation from among the following: I. Both divers are in free fall, and hence they will have the same splashdown speed. II. The divers have the same vertical speed at splashdown, but diver 2 has the greater horizontal speed. III. The diver who drops straight down gains more speed than the one who moves horizontally.

An archer shoots an arrow horizontally at a target 15 m away. The arrow is aimed directly at the center of the target, but it hits 52 cm lower. What was the initial speed of the arrow?

Victoria Falls The great, gray-green, greasy Zambezi River ows over Victoria Falls in south central Africa. The falls are approximately 108 m high. If the river is owing horizontally at 3.60 m/s just before going over the falls, what is the speed of the water when it hits the bottom? Assume the water is in free fall as it drops.

A diver runs horizontally off the end of a diving board with an initial speed of 1.85 m/s. If the diving board is 3.00 m above the water, what is the divers speed just before she enters the water?

An astronaut on the planet Zircon tosses a rock horizontally with a speed of 6.95 m/s. The rock falls through a vertical distance of 1.40 m and lands a horizontal distance of 8.75 m from the astronaut. What is the acceleration of gravity on Zircon?

Pitchers Mounds Pitchers mounds are raised to compensate for the vertical drop of the ball as it travels a horizontal distance of 18 m to the catcher. (a) If a pitch is thrown horizontally with an initial speed of 32 m/s, how far does it drop by the time it reaches the catcher? (b) If the speed of the pitch is increased, does the drop distance increase, decrease, or stay the same? Explain. (c) If this baseball game were to be played on the Moon, would the drop distance increase, decrease, or stay the same? Explain.

Playing shortstop, you pick up a ground ball and throw it to second base. The ball is thrown horizontally, with a speed of 22 m/s, directly toward point A (Figure 413). When the ball reaches the second baseman 0.45 s later, it is caught at point B. (a)How far were you from the second baseman? (b)What is the distance of vertical drop, AB?

A crow is ying horizontally with a constant speed of 2.70 m/swhen it releases a clam from its beak (Figure 414). The clam lands on the rocky beach 2.10 s later. Just before the clam lands, what is (a) its horizontal component of velocity, and (b) its vertical component of velocity? (c) How would your answers to parts (a) and (b) change if the speed of the crow were increased? Explain.

Amountain climber jumps a 2.8-m-wide crevasse by leaping horizontally with a speed of 7.8 m/s. (a) If the climbers direction of motion on landing is , what is the height difference between the two sides of the crevasse? (b) Where does the climber land?

A white-crowned sparrow ying horizontally with a speed of 1.80 m/s folds its wings and begins to drop in free fall. (a) How far does the sparrow fall after traveling a horizontal distance of 0.500 m? (b) If the sparrows initial speed is increased, does the distance of fall increase, decrease, or stay the same?

Pumpkin Toss In Denver, children bring their old jack-olanterns to the top of a tower and compete for accuracy in hitting a target on the ground (Figure 415). Suppose that the tower is 9.0 m high and that the bulls-eye is a horizontal distance of 3.5 m from the launch point. If the pumpkin is thrown horizontally, what is the launch speed needed to hit the bulls-eye?

If, in the previous problem, a jack-o-lantern is given an initial horizontal speed of 3.3 m/s, what are the direction and magnitude of its velocity (a) 0.75 s later, and (b) just before it lands?

Fairgoers ride a Ferris wheel with a radius of 5.00 m (Figure 416). The wheel completes one revolution every 32.0 s. (a) What is the average speed of a rider on this Ferris wheel? (b)If a rider accidentally drops a stuffed animal at the top of the wheel, where does it land relative to the base of the ride? (Note: The bottom of the wheel is 1.75 m above the ground.)

A swimmer runs horizontally off a diving board with a speed of 3.32 m/s and hits the water a horizontal distance of 1.78 m from the end of the board. (a)How high above the water was the diving board? (b) If the swimmer runs off the board with a reduced speed, does it take more, less, or the same time to reach the water?

Baseball and the Washington Monument On August 25, 1894, Chicago catcher William Schriver caught a baseball thrown from the top of the Washington Monument (555 ft, 898 steps). (a) If the ball was thrown horizontally with a speed of 5.00 m/s, where did it land? (b)What were the balls speed and direction of motion when caught?

Abasketball is thrown horizontally with an initial speed of 4.20 m/s (Figure 417). A straight line drawn from the release point to the landing point makes an angle of 30.0with the horizontal. What was the release height?

Aball rolls off a table and falls 0.75 m to the oor, landing with a speed of 4.0 m/s. (a) What is the acceleration of the ball just before it strikes the ground? (b) What was the initial speed of the ball? (c) What initial speed must the ball have if it is to land with a speed of 5.0 m/s?

A certain projectile is launched with an initial speed . At its highest point its speed is . What was the launch angle of the projectile? A. 30 B. 45 C. 60 D. 75

Three projectiles (A, B, and C) are launched with the same initial speed but with different launch angles, as shown in Figure 418. Rank the projectiles in order of increasing (a) horizontal component of initial velocity and (b) time of ight. Indicate ties where appropriate.

Three projectiles (A, B, and C) are launched with different initial speeds so that they reach the same maximum height, as shown in Figure 419. Rank the projectiles in order of increasing (a)initial speed and (b)time of ight. Indicate ties where appropriate.

A second baseman tosses the ball to the rst baseman, who catches it at the same level from which it was thrown. The throw is made with an initial speed of 18.0 m/s at an angle of 37.5 above the horizontal. (a) What is the horizontal component of the balls velocity just before it is caught? (b) How long is the ball in the air?

Referring to the previous problem, what are the ycomponent of the balls velocity and its direction of motion just before it is caught?

Acork shoots out of a champagne bottle at an angle of 35.0 above the horizontal. If the cork travels a horizontal distance of 1.30 m in 1.25 s, what was its initial speed?

Asoccer ball is kicked with a speed of 9.85 m/s at an angle of 35.0 above the horizontal. If the ball lands at the same level from which it was kicked, how long was it in the air?

In a game of basketball, a forward makes a bounce pass to the center. The ball is thrown with an initial speed of 4.3 m/s at an angle of 15below the horizontal. It is released 0.80 m above the oor. What horizontal distance does the ball cover before bouncing?

Repeat the previous problem for a bounce pass in which the ball is thrown 15 above the horizontal.

Snowballs are thrown with a speed of 13 m/s from a roof 7.0 m above the ground. Snowball A is thrown straight downward snowball B is thrown in a direction 25 above the horizontal. (a) Is the landing speed of snowball Agreater than, less than, or the same as the landing speed of snowball B? Explain. (b) Verify your answer to part (a) by calculating the landing speed of both snowballs.

In the previous problem, nd the direction of motion of the two snowballs just before they land.

A golfer gives a ball a maximum initial speed of 34.4 m/s. (a) What is the longest possible hole-in-one for this golfer? Neglect any distance the ball might roll on the green and assume that the tee and the green are at the same level. (b) What is the minimum speed of the ball during this hole-in-one shot?

What is the highest tree the ball in the previous problem could clear on its way to the longest possible hole-in-one?

The hang time of a punt is measured to be 4.50 s. If the ball was kicked at an angle of 63.0 above the horizontal and was caught at the same level from which it was kicked, what was its initial speed?

In a friendly game of handball, you hit the ball essentially at ground level and send it toward the wall with a speed of 18 m/s at an angle of 32 above the horizontal. (a) How long does it take for the ball to reach the wall if it is 3.8 m away? (b) How high is the ball when it hits the wall?

In the previous problem, (a)what are the magnitude and direction of the balls velocity when it strikes the wall? (b) Has the ball reached the highest point of its trajectory at this time? Explain.

A passenger on the Ferris wheel described in Problem 21 drops his keys when he is on the way up and at the 10 oclock position. Where do the keys land relative to the base of the ride?

On a hot summer day, a young girl swings on a rope above the local swimming hole (Figure 420). When she lets go of the rope her initial velocity is 2.25 m/s at an angle of 35.0 above the horizontal. If she is in ight for 0.616 s, how high above the water was she when she let go of the rope?

Acertain projectile is launched with an initial speed . At its highest point its speed is What was the launch angle?

Punkin Chunkin In Sussex County, Delaware, a postHalloween tradition is Punkin Chunkin, in which contestants build cannons, catapults, trebuchets, and other devices to launch pumpkins and compete for the greatest distance. Though hard to believe, pumpkins have been projected a distance of 4086 feet in this contest. What is the minimum initial speed needed for such a shot?

A dolphin jumps with an initial velocity of 12.0 m/s at an angle of 40.0above the horizontal. The dolphin passes through the center of a hoop before returning to the water. If the dolphin is moving horizontally when it goes through the hoop, how high above the water is the center of the hoop?

Aplayer passes a basketball to another player who catches it at the same level from which it was thrown. The initial speed of the ball is 7.1 m/s, and it travels a distance of 4.6 m. What were (a) the initial direction of the ball and (b) its time of ight?

Agolf ball is struck with a ve iron on level ground. It lands 92.2 m away 4.30 s later. What were (a)the direction and (b)the magnitude of the initial velocity?

A Record TossBabe Didrikson holds the world record for the longest baseball throw (296 ft) by a woman. For the following questions, assume that the ball was thrown at an angle of 45.0 above the horizontal, that it traveled a horizontal distance of 296 ft, and that it was caught at the same level from which it was thrown. (a)What was the balls initial speed? (b)How long was the ball in the air?

In the photograph to the left on page 87, suppose the cart that launches the ball is 11 cm high. Estimate (a)the launch speed of the ball and (b) the time interval between successive stroboscopic exposures.

Predict/Explain You throw a ball into the air with an initial speed of 10 m/s at an angle of 60 above the horizontal. The ball returns to the level from which it was thrown in the time T. (a) Referring to Figure 421, which of the plots (A, B, or C) best represents the speed of the ball as a function of time? (b) Choose the best explanation from among the following: I. Gravity causes the balls speed to increase during its ight. II. The ball has zero speed at its highest point. III. The balls speed decreases during its ight, but it doesnt go to zero.

Volcanoes on Io Astronomers have discovered several volcanoes on Io, a moon of Jupiter. One of them, named Loki, ejects lava to a maximum height of . (a)What is the initial speed of the lava? (The acceleration of gravity on Io is .) (b) If this volcano were on Earth, would the maximum height of the ejected lava be greater than, less than, or the same as on Io? Explain.

Asoccer ball is kicked with an initial speed of 10.2 m/s in a direction 25.0 above the horizontal. Find the magnitude and direction of its velocity (a) 0.250 s and (b) 0.500 s after being kicked.(c)Is the ball at its greatest height before or after 0.500 s? Explain.

Asecond soccer ball is kicked with the same initial speed as in Problem 53. After 0.750 s it is at its highest point. What was its initial direction of motion?

Agolfer tees off on level ground, giving the ball an initial speed of 46.5 m/s and an initial direction of 37.5above the horizontal. (a) How far from the golfer does the ball land? (b) The next golfer in the group hits a ball with the same initial speed but at an angle above the horizontal that is greater than 45.0. If the second ball travels the same horizontal distance as the rst ball, what was its initial direction of motion? Explain.

One of the most popular events at Highland games is the hay toss, where competitors use a pitchfork to throw a bale of hay over a raised bar. Suppose the initial velocity of a bale of hay is (a) After what minimum time is its speed equal to 5.00 m/s? (b)How long after the hay is tossed is it moving in a direction that is 45.0 below the horizontal? (c) If the bale of hay is tossed with the same initial speed, only this time straight upward, will its time in the air increase, decrease, or stay the same? Explain.

Child 1 throws a snowball horizontally from the top of a roof; child 2 throws a snowball straight down. Once in ight, is the acceleration of snowball 2 greater than, less than, or equal to the acceleration of snowball 1?

The penguin to the left in the accompanying photo is about to land on an ice oe. Just before it lands, is its speed greater than, less than, or equal to its speed when it left the water?

Predict/Explain Aperson ips a coin into the air and it lands on the ground a few feet away. (a) If the person were to perform an identical coin ip on an elevator rising with constant speed, would the coins time of ight be greater than, less than, or equal to its time of ight when the person was at rest? (b) Choose the best explanation from among the following: I. The oor of the elevator is moving upward, and hence it catches up with the coin in mid ight. , and the elevators speed doesnt change during the coins ight. III. The coin starts off with a greater upward speed because of the elevator, and hence it reaches a greater height.

Predict/Explain Suppose the elevator in the previous problem is rising with a constant upward acceleration, rather than constant velocity. (a) In this case, would the coins time of ight be greater than, less than, or equal to its time of ight when the person was at rest? (b) Choose the best explanation from among the following: I. The coin has the same acceleration once it is tossed, whether the elevator accelerates or not. II. The elevators upward speed increases during the coins ight, and hence it catches up with the coin at a greater height than before. III. The coins downward acceleration is less than before because the elevators upward acceleration partially cancels it.

Atrain moving with constant velocity travels 170 m north in 12 s and an undetermined distance to the west. The speed of the train is 32 m/s. (a) Find the direction of the trains motion relative to north. (b) How far west has the train traveled in this time?

Referring to Example 42, nd (a) the x component and (b) the y component of the hummingbirds velocity at the time . (c) What is the birds direction of travel at this time, relative to the positive x axis?

A racket ball is struck in such a way that it leaves the racket with a speed of 4.87 m/s in the horizontal direction. When the ball hits the court, it is a horizontal distance of 1.95 m from the racket. Find the height of the racket ball when it left the racket.

Ahot-air balloon rises from the ground with a velocity of . Achampagne bottle is opened to celebrate takeoff, expelling the cork horizontally with a velocity of relative to the balloon. When opened, the bottle is 6.00 m above the ground. (a)What is the initial velocity of the cork, as seen by an observer on the ground? Give your answer in terms of the x andyunit vectors. (b)What are the speed of the cork and its initial direction of motion as seen by the same observer? (c)Determine the maximum height above the ground attained by the cork. (d) How long does the cork remain in the air?

Repeat the previous problem, this time assuming that the balloon is descending with a speed of 2.00 m/s.

A soccer ball is kicked from the ground with an initial speed of 14.0 m/s. After 0.275 s its speed is 12.9 m/s. (a) Give a strategy that will allow you to calculate the balls initial direction of motion. (b) Use your strategy to nd the initial direction.

A particle leaves the origin with an initial velocity , and moves with constant acceleration . (a) How far does the particle move in the x direction before turning around? (b) What is the particles velocity at this time? (c)Plot the particles position at , 1.00 s, 1.50 s, and 2.00 s. Use these results to sketch position versus time for the particle.

When the dried-up seed pod of a scotch broom plant bursts open, it shoots out a seed with an initial velocity of 2.62 m/s at an angle of 60.5 above the horizontal. If the seed pod is 0.455 m above the ground, (a) how long does it take for the seed to land? (b)What horizontal distance does it cover during its ight?

Referring to Problem 68, a second seed shoots out from the pod with the same speed but with a direction of motion 30.0below the horizontal. (a) How long does it take for the second seed to land? (b)What horizontal distance does it cover during its ight?

Ashot-putter throws the shot with an initial speed of 12.2 m/s from a height of 5.15 ft above the ground. What is the range of the shot if the launch angle is (a) 20.0, (b) 30.0, or (c) 40.0?

Pararescue Jumpers Coast Guard pararescue jumpers are trained to leap from helicopters into the sea to save boaters in distress. The rescuers like to step off their helicopter when it is ten and ten, which means that it is ten feet above the water and moving forward horizontally at ten knots. What are (a) the speed and (b) the direction of motion as a pararescuer enters the water following a ten and ten jump?

Aball thrown straight upward returns to its original level in 2.75 s. A second ball is thrown at an angle of 40.0 above the horizontal. What is the initial speed of the second ball if it also returns to its original level in 2.75 s?

To decide who pays for lunch, a passenger on a moving train tosses a coin straight upward with an initial speed of 4.38 m/s and catches it again when it returns to its initial level. From the point of view of the passenger, then, the coins initial velocity is . The trains velocity relative to the ground is . (a) What is the minimum speed of the coin relative to the ground during its ight? At what point in the coins ight does this minimum speed occur? Explain. (b)Find the initial speed and direction of the coin as seen by an observer on the ground. (c)Use the expression for derived in Example 47 to calculate the maximum height of the coin, as seen by an observer on the ground. (d)Calculate the maximum height of the coin from the point of view of the passenger, who sees only one-dimensional motion.

Acannon is placed at the bottom of a cliff 61.5 m high. If the cannon is red straight upward, the cannonball just reaches the top of the cliff. (a)What is the initial speed of the cannonball? (b)Suppose a second cannon is placed at the top of the cliff. This cannon is red horizontally, giving its cannonballs the same initial speed found in part (a). Show that the range of this cannon is the same as the maximum range of the cannon at the base of the cliff. (Assume the ground at the base of the cliff is level, though the result is valid even if the ground is not level.)

Shot Put Record The mens world record for the shot put, 23.12 m, was set by Randy Barnes of the United States on May 20, 1990. If the shot was launched from 6.00 ft above the ground at an initial angle of 42.0, what was its initial speed?

Referring to Conceptual Checkpoint 43, suppose the two snowballs are thrown from an elevation of 15 m with an initial speed of 12 m/s. What is the speed of each ball when it is 5.0 m above the ground?

A hockey puck just clears the 2.00-m-high boards on its way out of the rink. The base of the boards is 20.2 m from the point where the puck is launched. (a)Given the launch angle of the puck, , outline a strategy that you can use to nd its initial speed, .

Referring to Active Example 42, suppose the ball is punted from an initial height of 0.750 m. What is the initial speed of the ball in this case?

A LobPass Versus a BulletAquarterback can throw a receiver a high, lazy lob pass or a low, quick bullet pass. These passes are indicated by curves 1 and 2, respectively, in Figure 422. (a) The lob pass is thrown with an initial speed of 21.5 m/s and its time of ight is 3.97 s. What is its launch angle? (b)The bullet pass is thrown with a launch angle of 25.0. What is the initial speed of this pass? (c) What is the time of ight of the bullet pass?

Collision Course Auseful rule of thumb in boating is that if the heading from your boat to a second boat remains constant, the two boats are on a collision course. Consider the two boats shown in Figure 423. At time , boat 1 is at the location (X, 0) and moving in the positive ydirection; boat 2 is at (0, Y) and moving in the positive xdirection. The speed of boat 1 is . (a)What speed must boat 2 have if the boats are to collide at the point (X, Y)? (b) Assuming boat 2 has the speed found in part (a), calculate the displacement from boat 1 to boat 2, . (c) Use your results from part (b) to show that , independent of time. This shows that maintains a constant direction until the collision, as specied in the rule of thumb.

As discussed in Example 47, the archersh hunts by dislodging an unsuspecting insect from its resting place with a stream of water expelled from the shs mouth. Suppose the archersh squirts water with a speed of 2.15 m/s at an angle of 52.0 above the horizontal, and aims for a beetle on a leaf 3.00 cm above the waters surface. (a)At what horizontal distance from the beetle should the archersh re if it is to hit its target in the least time? (b) How much time will the beetle have to react?

(a)What is the greatest horizontal distance from which the archersh can hit the beetle, assuming the same squirt speed and direction as in Problem 81? (b) How much time does the beetle have to react in this case?

Find the launch angle for which the range and maximum height of a projectile are the same.

A mountain climber jumps a crevasse of width W by leaping horizontally with speed . (a)If the height difference between the two sides of the crevasse is h, what is the minimum value of for the climber to land safely on the other side? (b) In this case, what is the climbers direction of motion on landing?

Prove that the landing speed of a projectile is independent of launch angle for a given height of launch.

Maximum Height and Range Prove that the maximum height of a projectile, H, divided by the range of the projectile, R, satises the relation .

Landing on a Different LevelAprojectile red from with initial speed and initial angle lands on a different level, . Show that the time of ight of the projectile is where is the time of ight for and H is the maximum height of the projectile.

Amountain climber jumps a crevasse by leaping horizontally with speed . If the climbers direction of motion on landing is below the horizontal, what is the height difference hbetween the two sides of the crevasse?

Referring to Problem 73, suppose the initial velocity of the coin tossed by the passenger is . The trains velocity relative to the ground is still .(a)What is the minimum speed of the coin relative to the ground during its ight? At what point in the coins ight does this minimum speed occur? Explain. (b) Find the initial speed and direction of the coin as seen by an observer on the ground. (c) Use the expression for derived in Example 47 to calculate the maximum height of the coin, as seen by an observer on the ground. (d)Repeat part (c) from the point of view of the passenger. Verify that both observers calculate the same maximum height.

Projectiles: Coming or Going? Most projectiles continually move farther from the origin during their ight, but this is not the case if the launch angle is greater than . For example, the projectile shown in Figure 424 has a launch angle of 75.0and an initial speed of 10.1 m/s. During the portion of its motion shown in red, it is moving closer to the origin it is moving away on the blue portions. Calculate the distance from the origin to the projectile (a) at the start of the red portion, (b) at the end of the red portion, and (c) just before the projectile lands. Notice that the distance for part (b) is the smallest of the three.

What is the maximum height of a rover between its rst and second bounces? A. 2.58 m B. 4.68 m C. 12.3 m D. 148 m

How much time elapses between the rst and second bounces? A. 1.38 s B. 2.58 s C. 5.15 s D. 5.33 s

How far does a rover travel in the horizontal direction between its rst and second bounces? A. 13.2 m B. 49.4 m C. 51.1 m D. 98.7 m

What is the average velocity of a rover between its rst and second bounces? A. 0 B. 2.57 m/s in the x direction C. 9.92 m/s at 75.0 above the x axis D. 9.58 m/s in the y direction

Referring to Example 45 (a)At what launch angle greater than 54.0 does the golf ball just barely miss the top of the tree in front of the green? Assume the ball has an initial speed of 13.5 m/s, and that the tree is 3.00 m high and is a horizontal distance of 14.0 m from the launch point. (b) Where does the ball land in the case described in part (a)? (c)At what launch angle less than 54.0 does the golf ball just barely miss the top of the tree in front of the green? (d) Where does the ball land in the case described in part (c)?

Referring to Example 45 Suppose that the golf ball is launched with a speed of 15.0 m/s at an angle of 57.5above the horizontal, and that it lands on a green 3.50 m above the level where it was struck. (a) What horizontal distance does the ball cover during its ight? (b)What increase in initial speed would be needed to increase the horizontal distance in part (a) by 7.50 m? Assume everything else remains the same.

Referring to Example 46 Suppose the ball is dropped at the horizontal distance of 5.50 m, but from a new height of 5.00 m. The dolphin jumps with the same speed of 12.0 m/s. (a) What launch angle must the dolphin have if it is to catch the ball? (b)At what height does the dolphin catch the ball in this case? (c) What is the minimum initial speed the dolphin must have to catch the ball before it hits the water?

Referring to Example 46 Suppose we change the dolphins launch angle to 45.0, but everything else remains the same. Thus, the horizontal distance to the ball is 5.50 m, the drop height is 4.10 m, and the dolphins launch speed is 12.0 m/s. (a) What is the vertical distance between the dolphin and the ball when the dolphin reaches the horizontal position of the ball? We refer to this as the miss distance. (b) If the dolphins launch speed is reduced, will the miss distance increase, decrease, or stay the same? (c) Find the miss distance for a launch speed of 10.0 m/s.