Open-Response Homework Problem 18.3 You and your friend are playing racketball a

Question

Open-Response Homework Problem 18.3 You and your friend are playing racketball at the HPER. You are standing 7m from the wall, and you hit the ball towards it at a 30 degree angle above the horizontal, with a speed of 15 m/s. The ball leaves the racket at a height of 1.5 m. How long does it take the ball to hit the wall? How high up the wall does the ball hit? What are the horizontal and vertical components of the velocity of the ball just before it hits the wall? When it hits, has it passed the highest point in its trajectory? Considering the system as the Earth and the ball, complete the work-energy diagram for the system for the time from just after it leaves your hand until just before it hits the wall. Considering the system as the just the ball, complete the work-energy diagram below for the system for the time from just after it leaves your hand until just before it hits the wall.

Explanation / Answer

Here ,

a) time taken to hit the wall ,

time = distance /speed

time = 7/(15 * cos(30))

time = 0.54 s

the time taken to hit the wall is 0.54 s

b)

let the height is h

Using second equation of motion

h = 1.5 + 15 * sin(30) * 0.54 - 0.5 * 9.8 * 0.54^2

solving for h

h = 4.12 m

the ball hit the wall at 4.12 high point

c)

Here , horizontal component of velocity = vo*cos(theta)

horizontal component of velocity = 15 * cos(30)

horizontal component of velocity = 13 m/s

vertical component of velocity = 15 * sin(30) - 9.8 * 0.54

vertical component of velocity = 2.21 m/s

d)

time taken to reach the highest point , t = v*sin(theta)/g

t = 15 * sin(30)/9.8

t = 0.765 s

as the time taken to reach the maximum height is more than the time taken to hit the walls .

Hence , the ball has not passed it's highest point

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