Hello, Please show me how to work out the problem step by step. Thanks! 15. A te

Question

Hello,

Please show me how to work out the problem step by step. Thanks!

15. A tennis player hits a ball at ground level, giving it an initial velocity of 24 m/s at 57 degree above the horizontal. (a) What are the horizontal and vertical components of the ball?s initial velocity? (b) How high above the ground does the ball go? (C) How long does it take the ball to reach its maximum height? (d) What are the ball?s velocity and acceleration at its highest point? (e) For how long a time is the ball in the air? (f) When this ball lands on the court, how far is it from the place where it was hit?

Explanation / Answer

A) Anyway, the horizontal component can be figured out by taking the initial velocity and multiplying it by the cosine of the angle, which would be 24 x cos(57) = 21.5m/s

B) You can use the formula Vf^2 = Vi^2+2ad to figure out how the ball goes. The initial velocity would be from the y component, which is the initial velocity multiplied by the sin of the angle. 24 m/s x sin(57) = 10.4m/s

Vf^2 = Vi^2+2ad
(0m/s)^2 = (21.5 m/s)^2 + 2(-9.8)(d)
d = 23.5m

C) You can use the vf = vi + at formula to find out the time.
vf = vi + at
0 m/s = 21.5 m/s + -9.8m/s^2(t)
t = 1.09s

D) The velocity at the highest point is 10.4 m/s because the Vertical velocity is 0 and the horizontal velocity is constant.

E) You can use the d = vit + (1/2)at^2 to solve for time.
d = 0 m
vi = 21.5 m/s
a = 9.8
t = ?

d = vit + (1/2)at^2
0m = 21.5t + (1/2)(9.8m/s^2)t^2
t = 4.4s
or you could multiply the answer in part c by two because the amount of time it takes to reach the maximum point is tantamount to the amount of time it takes to reach the ground again if the height of the final and initial ground are the same.

F) This deals only with horizontal motion.
vix = 10.5 (taken from (A))
d = ?
t = 4.4s
a = 0m/s^2

Acceleration is always 0 for horizontal projectiles in mid-air. The amount of time it takes for the ball to travel without horizontal motion is equal to with horizontal motion

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