During a tennis match, a player serves the ball at 24.3 m/s, with the center of

Question

During a tennis match, a player serves the ball at 24.3 m/s, with the center of the ball leaving the racquet horizontally 2.31 m above the court surface. The net is 12.0 m away and 0.900 m high. When the ball reaches the net, (a) what is the distance between the center of the ball and the top of the net? (b) Suppose that, instead, the ball is served as before but now it leaves the racquet at 5.00° below the horizontal. When the ball reaches the net, what now is the distance between the center of the ball and the top of the net? Enter a positive number if the ball clears the net. If the ball does not clear the net, your answer should be a negative number.

Explanation / Answer

a)

Consider the motion in horizontal direction

Vox = initial velocity = 24.3 m/s

X = displacement in horizontal direction = 12 m

t = time taken

using the equation

t = X/Vox = 12 /24.3 = 0.494 sec

consider the motion in vertical direction

Voy = initial velocity = 0 m/s

Y = displacement

a = acceleration = 9.8

using the equation

Y = Voy t + (0.5) a t2

Y = 0 (0.494) + (0.5) ( 9.8) (0.494)2

Y = 1.2 m

ball position relative to floor = 2.31 - 1.2 = 1.11 m

distance between top of net and ball = 1.11 - 0.9 = 0.21 m

b)

Consider the motion in horizontal direction

Vox = initial velocity = 24.3 cos5 = 24.2 m/s

X = displacement in horizontal direction = 12 m

t = time taken

using the equation

t = X/Vox = 12 /24.2 = 0.496 sec

consider the motion in vertical direction

Voy = initial velocity = 24.3 Sin5 = 2.12 m/s

Y = displacement

a = acceleration = 9.8

using the equation

Y = Voy t + (0.5) a t2

Y = (2.12) (0.494) + (0.5) ( 9.8) (0.494)2

Y = 2.24 m

ball position relative to floor = 2.31 - 2.24 = 0.07 m

distance between top of net and ball = 0.07 - 0.90 = - 0.83 m

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