A ball is fired from a cannon at point I and follows the trajectoryshown in Figure

a. Can a vector have nonzero magnitude if a component is zero? If no, why not? If yes, give an example. b. Can a vector have zero magnitude and a nonzero component? If no, why not? If yes, give an example.

Ts it possible to add a scalar to a vector? If so, demons trate. If not, explain why not.

Suppose two vectors have unequal magnitudes. Can their sum be O? Explain.

Suppose C =A+ ii. a. Under what circumstances does C = A + B? b. Could C = A - B? If so, how? If not, why not?

For a projectile, which of the following quantities are constant during the flight: x, y, v.,, v_, , v, a,, ay? Which of the quantities are zero throughout the flight?

A baseball player throws a ball at a 40 angle to the ground. The ball lands on the ground some distance away. a. Is there any point on the trajectory where ii and a are parallel to each othe r? If so, where? b. Ts there any point where ii and a are perpendicular to each other? If so, where?

An athlete performing the long jump tries to achieve the maximum distance from the point of takeoff to the fi rst point of touching the ground. After the jump, rather than land upright, she extends her legs forward as in the photo. How does this affect the time in the air? How does this give the jumper a longer range?

A person trying to throw a ball as far as possible will run forward during the throw. Explain why this increases the distance of the throw.

If you kick a football, at what angle to the ground should you kick the ball for the maximum range- that is, the greatest distance down the field? At what angle to the ground should you kick the ball for the maximum "hang time"-that is, the maximum time in the air?

A passenger on a jet ai rplane c laims to be able to walk at a speed in excess of 500 mph. Can this be true? Explain.

If you go to a ski area, you' ll likely find that the begi nner's slope has the smallest angle. Use the concept of acceleration on a ramp to explain why this is so.

In an amusement-park ride, cars rolling along at high speed suddenly head up a long, straight ramp. They roll up the ramp, reverse direction at the highest point, then roll backward back down the ramp. Tn each of the following segments of the motion, which way does the acceleration vector point? a. As the cars roll up the ramp. b. At the highest point on the ramp. c. As the cars roll back down the ramp.

There are competitions in which pilots fly small planes low over lhe ground and drop weights, trying to hit a target. A pilot flying low and slow drops a weight; it takes 2.0 s to hit the ground, dming which it travels a hrnizontal distance of I 00 m. Now lhe pilot does a mn at the same height but twice the speed. How much time does it take the weight to hit the ground? How far does it travel before it lands?

A cyclist goes around a level, circular track at constant speed. Do you agree or disagree with the following statement: "Because the cyc li st's speed is constant, her acceleration is zero." Explai n.

You are cycling around a circular track at a constant speed. Does the magnitude of your acceleration change? The direction?

An airplane has been directed to fly in a clockwise circle, as seen from above, at constant speed until another plane has landed. When the plane is going north, is it accelerating? ff so, in what direction does the acceleration vector point? If not, why not?

When you go around a corner in your car, your car follows a path that is a segment of a circle. To turn safely, you should keep your car's acceleration below some safe upper limit. If you want to make a " tighter" turn- that is, turn in a circle with a smaller radius-how should you adjust your speed? Explain.

Which combination of the vectors shown in Figure Q3. I 8 has the ~rge~t m~gnitude? A. A + B + C B. ii +i\ -c c. if -ii+ c D. B- A - C

Two vectors appear as in Figure Q3. I 9. Which combination points directly to the left? A. P+Q B. P- Q c. Q-? D. - Q- P

The gas pedal in a car is sometimes referred to as "the accelerator." Which other cont rols on the vehicle can be used to produce acce leration? A. The brakes. C. The gear shift. B. The steering wheel. D. All of the above.

A car travels at constant speed along the curved path shown from above in Figure Q3.2 l. Five possible vectors are also shown in the figure; the letter E represents the zero vector. Which vector best represents a. The car's velocity at position I? b. The car's acceleration at posi tion I? c. The car's velocity at position 2? d. The car's acceleration at position 2? e. The car's velocity at position 3? f. The car's acceleration at position 3?

A ball is fired from a cannon at point I and follows the trajectory shown in Figure Q3.22. Air resistance may be neglected. Five possible vectors are also shown in the figure; the letter E represents the zero vector. Which vector best represents a. The ball's velocity at position 2? b. The ball's acceleration at position 2? c. The ball's velocity at position 3? d. The ball's acceleration at position 3?

A ball thrown at an initial angle of 37.0 and initial velocity of 23.0 mis reaches a maximum height h, as shown in Figure Q3.23. With what initial speed must a ball be thrown straight up to reach the same maximum height h? A. 13.8 mis B. 17.3 mis C. 18.4 m/s D. 23.0 mis

A cannon elevated at 40 is fired at a wall 300 m away on level ground, as shown in Figure Q3.24. The initial speed of the cannonball is 89 m/s. a. How long does it take for the ball to hit the wall? A. 1.3 s B. 3.3 s C. 4.4 s D. 6.8 s E. 7.2 s b. At what height h does the ball hit the wall? A. 39 m B. 47 m C. 74 m D. 160m E. 210m

A car drives horizontally off a 73-m-high cliff at a speed of 27 m/s. Ignore air resistance. a. How long will it take the car to hit the ground? A. 2.0 s B. 3.2 s C. 3.9 s D. 4.9 s E. 5.0 s b. Approximately how far from the base of the cliff will the car hit? A.751JJ B.90m C. IOOm D. 170 m E. 280 m

A football is kicked at an angle of 30 with a speed of 20 mis. To the nearest second, how Jong will the ball stay in the air? A. I s B. 2 s c. 3 s D. 4 s

A football is kicked at an angle of 30 with a speed of 20 mis. To the nearest 5 m, how far wi II the ball travel? A. 15m B. 25m C. 35 m D. 45 m

Riders on a Ferris wheel move in a circle with a speed of 4.0 mis. As they go around, they experience a centripetal acceleration of 2.0 mls2 . What is the diameter of this particular Ferris wheel? A. 4.0 m B. 6.0 m C. 8.0 m D. 16m E. 24 m

Formula One race cars are capable of remarkable accelerations when speeding up, slowi ng down, and turning corners. At one track, cars round a corner that is a segment of a circle of radius 95 mat a speed of 68 mis. What is the approximate magnitude of the centripetal acceleration, in units of g? A. lg B. 2g C. 3g D. 4g E. 5g

On a day when the water is flowing relatively gently, water in the Niagara River is moving horizontally at 4.5 mis before shooting over Niagara Falls. After moving over the edge, the water drops 53 m to the water below. If we ignore air resistance, how much time does it take for the water to go from the top of the falls to the bottom? How far does the water move horizontally during this time?

Two spheres are both launched horizontally from a 1.0-m-high table. Sphere A is launched with an initial speed of 5.0 mis. Sphere B is launched with an initial speed of 2.5 mis. a. What are the times for each sphere to hit the floor? b. What are the distances that each travels from the edge of the table?

A rifle is aimed horizontally at a target 50 m away. The bullet hits the target 2.0 cm below the aim point. a. What was the bullet's flight time? b. What was the bullet's speed as it left the barrel?

A gray kangaroo can bound across a flat stretch of ground BIO with each jump carrying it I 0 m from the takeoff poi nt. If the kangaroo leaves the ground at a 20 angle, what are its (a) takeoff speed and (b) horizontal speed?

On the Apollo 14 m1ss1on to the moon, astronaut Alan Shepard hit a golf ball with a golf club improvised from a tool. The free-fall acceleration on the moon is 1/6 of its value on earth. Suppose he hit the ball with a speed of 25 mis at an angle 30 above the horizontal. a . How long was the ball in flight? b. How far did it travel? c. Ignoring air resistance, how much farther would it travel on the moon than on earth?

A sprinkler mounted on the ground sends out ajet of water at a 30 angle to the horizontal. The water leaves the nozzle at a speed of 12 mis. How far does the water travel before it hits the ground?

A good quarterback can throw a football at 27 mis (about 60 mph). If we assume that the ball is caught at the same height from which it is thrown, and if we ignore air resistance, what is the maximum range in meters (which is approximately the same as the range in yards) of a pass at th is speed? How long is the ball in the air?

Racing greyhounds are capable of rounding corners at very BKl high speeds. A typical greyhound track has turns that are 45-m-diameter semicircles. A greyhound can run around these turns at a constant speed of 15 mis. What is its acceleration in mls2 and in units of g?

To withstand "g-fotces" of up to I 0 g's, caused by suddenly BKl pulling out of a steep dive, fighter jet pilots train on a "human centri fuge." IO g's is an acceleration of 98 mls2. If the length of the centrifuge arm is 12 .m, at what speed is the rider moving when she experiences 10 g's?

The Scion iQ is a compact car that is capable of very tight turns-it can spin around in a circle 8.0 min diameter. If a driver goes around such a circle at 5 mis (a bit faster than I 0 mph), what is the magnitude of his acceleration?

In a roundabout (or traffic circle), cars go around a 25-m-diameter circle. If a car's tires will skid when the car experiences a centripetal acceleration greater than 0.60g, what is the maximum speed of the car in this roundabout?

A particle rotates in a circle with centripetal acceleration a= 8.0 mls2 What is a if a. The radius is doubled without changing the particle's speed? b. The speed is doubled without changing the circle's radius?

Entrance and exit ramps for freeways are often circular stretches of road. As you go around one at a constant speed, you wi ll experience a constant acceleration. Suppose you drive through an entrance ramp at a modest speed and your acceleration is 3.0 mls2. What will be the acceleration if you double your speed?

A peregrine falcon in a tight, c ircular turn can attain a cenBKJ tripetal acceleration 1.5 times the free-fall acceleration. If the falcon is flying at 20 mis, what is the radius of the turn?

Suppose e =A+ jj where vector A has components Ax= 5, Ay = 2 and vector B has components Bx= -3, Bv = -5. a. What are the x- and y-components of vector e? b. Draw a coordinate system and on it show vectors A, B, and e. c. What are the magnitude and direction of vector C?

Suppose D =A - B where vector A has components Ax= 5, Ay = 2 and vector B has components Bx= - 3, By= -5. a. What are the x- and y-components of vector D? b. Draw a coordinate system and on it show vectors A, ii, and D. c. What are the magnitude and direction of vector D?

Suppose E = 2A + 3B where vector A has components A, = 5, Ay = 2 and vector iJ has components B,, = - 3, Bv = - 5. a. What are the x- and y-components of vector E? b. Draw a coordinate system and on it show vectors A, ii, and. c. What are the magnitude and direct.ion of vector E?

For the three vectors shown in r Figure P3.47, the vector sum i5 = A+ jj + e has components Dx = 2 and Dy = O. a. What are the x- and y-components of vector B? b. Write iJ as a magnitude and a direction.

Let A= (3.0 m, 20 south of east), jj = (2.0 m, north), and e = (5.0 m, 70 south of west). a. Draw and label A, ii, and e with their tails at the origin. Use a coordinate system with the x-axis to the east. b. Write the x- and y-components of vectors A, B, and e. c. Find the magnitude and the direction of D = A+ B + C.

A typical set of stairs is angled at 38. You climb a set of stairs at a speed of 3.5 mis. a. How much height wi ll you gain in 2.0 s? b. How much horizontal distance will you cover in 2.0 s?

A pilot in a small plane encounters shifting winds. He flies 26.0 km northeast, then 45.0 km due north. From this point, he flies an additional distance in an unknown direction, only to find himself at a small airstrip that his map shows to be 70.0 km directly north of his starting point. What were the length and direction of the third leg of his trip?

A small plane, I 00 km due south of the equator, is fl ying at 150 km/h with respect to the ground along a straight line 30 to the west of north. In how many minutes will the plane cross the equator?

The bacterium Escherichia coli (or . coli) is a single-celled BIO organism that lives in the gut of healthy humans and animals. When grown in a uniform medium rich in salts and amino acids, these bacteria swim along zig-zag paths at a constant speed of 20 ,mis. Figure P3.52 shows the trajectory of an E. coli as it moves from point A to point E. Each segment of the mot.ion can be identified by two letters, such as segment BC. a. For each of the four segments in the bacterium's trajectory, calculate the x- and y-components of its displacement and of its velocity. b. Calculate both the total distance traveled and the magnitude of the net displacement for the entire motion. c. What are the magnitude and the direction of the bacterium's average velocity for the entire trip?

A skier gliding across the snow at 3.0 mis suddenly starts down a !0 incline, reaching a speed of 15 mis at the bottom. Friction between the snow and her freshly waxed skies is negligible. a. What is the length of the incline? b. How long does it take her to reach the bottom?

A block slides along the frictionless track shown in Figure P3.54 with an initial speed of 5.0 mis. Assume it 1.0 m turns all the corners smoothly, FIGURE P3.54 with TIO loss of speed. What is the block's speed as it goes over the top?

When the moving sidewalk at the airport is broken, as it often seems to be, it takes you 50 s to walk from your gate to the baggage claim. When it is working and you stand on the moving sidewalk the entire way, without walking, it takes 75 s to travel the same distance. How long will it take you to travel from the gate to baggage claim if you walk while riding on the moving sidewalk?

Ships A and B leave port together. For the next two hours, ship A travels at 20 mph in a direction 30 west of north while ship B travels 20 east of north at 25 mph. a. What is the distance between the two ships two hours after they depart? b. What is the speed of ship A as seen by ship B?

A flock of ducks is trying to migrate south for the winter, but they keep being blown off course by a wind blowing from the west at 12 mis. A wise elder duck finally realizes that the solution is to fly at an angle to the wind. lfthe ducks can tly at 16 mis relative to the air, in what direction should they head in order to move directly south?

A kayaker needs to paddle north across a I 00-m-wide harbor. The tide is going out, creating a tidal current flowing east at 2.0 mis. The kayaker can paddle with a speed of 3.0 mis. a. In which direction should he paddle in order to travel straight across the harbor? b. How long will it take him to cross?

A plane has an airspeed of 200 mph. The pilot wishes to reach a destination 600 mi due east, but a wind is blowing at 50 mph in the direction 30 north of east. a. In what direction must the pi lot head the plane in order to reach her desti nation? b. How long will the trip take?

The Gulf Stream off the east coast of the United States can flow at a rapid 3.6 mis to the north. A ship in this current has a crui sing speed of 10 mis. The captain would li ke to reach land at a point due west from the current position. a. In what direction with respect to the water should the ship sail? b. At this heading, what is the ship's speed with respect to land?

A physics student on Planet Exidor throws a ball, and it fo llows the parabolic trajectory shown in Figure P3.6 I. The ball's position is shown at 1.0 s intervals until t = 3.0 s. At t = 1.0 s, the ball 's velocity has components vx = 2.0 mis, vy =2.0 mis. a. Determine the x- and y-components of the ball 's velocity at 1 = 0.0 s, 2.0 s, and 3.0 s. b. What is the value of g on Planet Exidor? c. What was the ball's launch angle?

A ball thrown horizontally at 25 mis travels a horizontal distance of 50 m before hitting the ground. From what height was the ball thrown?

In 1780, in what is now BIO referred to as "Brady's Leap," Captain Sam Brady of the U.S. Continental Army escaped certain death from his enemies by running horizontally off the edge of the cliff above Ohio's Cuyahoga River, which is confined at that spot to a gorge. He landed safely on the far side of the river. It was reported that he leapt 22 ft across while falling FIGURE PJ.GJ 20 ft. Tall tale, or possible? a. What is the minimum speed with which he'd need to run off the edge of the cliff to make it safely to the far side of the river? b. The world-record time for the 100 m dash is approximately 10 s. Given thi s, is it reasonable to expect Brady to be able to run fast enough to achieve Brady's leap?

The longest recorded pass in an NFL game traveled 83 yards in the air from the quarterback to the receiver. Assuming that the pass was thrown at the optimal 45 angle, what was the speed at which the ball left the quarterback's hand?

A spring-loaded gun, fi red vertically, shoots a marble 6.0 m straight up in the air. What is the marble's range if it is fired horizontally from 1.5 m above the ground?

Small-plane pilots regularly compete in "message drop" competitions, dropping heavy weights (for which air resistance can be ignored) from their low-flying planes and scoring points for having the weights land close to a target. A plane 60 m above the ground is flying directly toward a target at 45 m/s. a. At what distance from the target should the pilot drop the weight? b. The pilot looks down at the weight after she drops it. Where is the plane located at the instant the weight hits the ground- not yet over the target, directly over the target, or past the target?

In a shot-put event, an athlete throws the shot with an initial speed of 12.0 m/s at a 40.0 angle from the horizontal. The shot leaves her hand at a height of 1.80 m above the ground. a. How far does the shot travel? b. Repeat the calculation of part a for angles 42.5, 45.0, and 47.5. Put all your results, including 40.0, in a table. At what angle of release does she throw the farthest?

Trained dolphins are capable of a vertical leap of 7.0 m BIO straight up from the surface of the water-an impressive feat. INT Suppose you could train a dolphin to launch itself out of the water at this same speed but at an angle. What maximum horizontal range could the dolphin achieve?

A tennis player hits a ball 2.0 m above the ground. The ball leaves his racquet with a speed of 20 mis at an angle 5.0 above the horizontal. The horizontal distance to the net is 7.0 m, and the net is 1.0 m high. Does the ball clear the net? If so, by how much? Tf not, by how much does it miss?

The shot put is a trackINT and-field event in which athletes throw a heavy ballthe shot-as far as possible. The best athletes can throw the shot as far as 23 m. Athletes who use the "glide" technique push the shot outward in a reasonably straight line, accelerating it over a distance of about 2.0 m. What acceleration do they provide to the shot as they push on it? Assume that the shot is launched at an angle of 37, a reasonable value for an excellent throw. You can assume that the shot lands at the same height from which it is thrown; this simplifies the calculation considerably, and makes only a small difference in the final result.

Water at the top of Horseshoe Falls (part of Niagara Falls) is moving horizontally at 9.0 m/s as it goes off the edge and plunges 53 m to the pool below. If you ignore air resistance, at what angle is the falling water moving as it enters the pool?

A supply plane needs to drop a package of food to scientists working on a glacier in Greenland. Jhe plane flies 100 m above the glacier at a speed of 150 mis. How far short of the target should it drop the package?

A child slides down a fri ctionless 3.0-m-long playground slide tilted upward at an angle of 40. At the end of the slide, there is an additional section that curves so that the child is launched off the end of the slide horizontally. a. How fast is the child moving at the bottom of the sl ide? b. If the end of the slide is 0.40 m above the ground, how far from the end does she land?

A sports car is advertised as capable of "reaching 60 mph in INT 5 seconds flat, cornering at 0.85g, and stopping from 70 mph in only 168 feet." In which of those three situations is the magnitude of the car's acceleration the largest? In which is it the smallest?

A Ford Mustang can accelerate from 0 to 60 mph in a time of INT 5.6 s. A Mini Cooper isn' t capable of such a rapid start, but it can turn in a very small circle 34 ft in diameter. How fast would you need to drive the Mini Cooper in this tight circle to match the magnitude of the Mustang's acceleration?

The "Screaming Swing" is a carnival ride that is-not surprisingly-a giant swing. It's actually two swings moving in opposite directions. At the bottom of its arc, a rider in one swing is moving at 30 mis with respect to the ground in a 50-m-diameter circle. The rider in the other swi ng is moving in a similar circle at the same speed, but in the exact opposite direction. a. What is the acceleration, in mls2 and in units of g, that riders experience? b. At the bottom of the ride, as they pass each other, how fast do the riders move with respect to each other?

On an othe1wise straight stretch of road near Moffat, Colorado, the road suddenly turns. This bend in the road is a segment of a circle with radius 110 m. Drivers are cautioned to slow down to 40 mph as they navigate the curve. a. If you heed the sign and slow to 40 mph, what will be your acceleration going around the c urve at this constant speed? Give your answer in mls2 and in units of g. b. At what speed would your acceleration be double that at the recommended speed?

At the end of the first section of the motion, riders are moving at what approximate speed? A. 3 mis B. 6 mis C. 9 mis D. 12 mis

Suppose the acceleration during the second section of the motion is too large to be comfortable for riders. What change could be made to decrease the acceleration during this section? A. Reduce the radius of the circular segment. B. Increase the radius of the circular segment. C. Increase the angle of the ramp. D. Increase the length of the ramp.

What is the vertical component of the velocity of a rider as he or she hits the water? A. 2.4 mis B. 3.4 mis C. 5.2 mis D. 9.1 mis

Suppose the designers of the water slide want to adjust the height h above the water so that riders land twice as far away from the bottom of the slide. What would be the necessary height above the water? A. 1.2 m C. 2.4 m B. 1.8 m D. 3.0m

During which section of the motion is the magnitude of the acceleration experienced by a rider the greatest? A. The fir.st. B. The second. C. The thi rd. D. It is the same in all sections