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Answer: Projectile Motion on an Incline. Refer to the
Chapter 3, Problem 87P(choose chapter or problem)
Problem 87P
Projectile Motion on an Incline. Refer to the Bridging Problem in chapter 3. (a) An archer on ground that has a constant upward slope of 30.0° aims at a target 60.0 in farther up the incline. The arrow in the bow and the bull’s-eye at the center of the target are each 1.50 m above the ground. The initial velocity of the arrow just after it leaves the bow has magnitude 32.0 m/s. At what angle above the horizontal should the archer aim to hit the bull ’s–eye? If there are two such angles, calculate the smaller of the two. You might have to solve the equation for the angle by itcration — that is by trial and error. How does the angle compare to that required when the ground in level with slope? (b) Repeat the problem in ground that has a constant downward slope of 30.0°.
Questions & Answers
QUESTION:
Problem 87P
Projectile Motion on an Incline. Refer to the Bridging Problem in chapter 3. (a) An archer on ground that has a constant upward slope of 30.0° aims at a target 60.0 in farther up the incline. The arrow in the bow and the bull’s-eye at the center of the target are each 1.50 m above the ground. The initial velocity of the arrow just after it leaves the bow has magnitude 32.0 m/s. At what angle above the horizontal should the archer aim to hit the bull ’s–eye? If there are two such angles, calculate the smaller of the two. You might have to solve the equation for the angle by itcration — that is by trial and error. How does the angle compare to that required when the ground in level with slope? (b) Repeat the problem in ground that has a constant downward slope of 30.0°.
ANSWER:
Solution 87P
Step 1:
The horizontal displacement, X = vox t
The vertical displacement, Y = voyt - ½ gt2
vox = v cos𝜽 and voy = v sin𝜽
And we know that, vy = voy - gt (For upward motion)