3. A horizontally moving tennis ball barely clears the net, a distance y above the surface of the court. To land within the tennis court the ball must not be moving too fast.
a. To remain within the court’s border, a horizontal distance d from the bottom of the net, show that the ball’s maximum speed over the net is v = / √ 2
b. Suppose the height of the net is 1.00 m, and the court’s border is 12.0 m from the bottom of the net. Use g = 10 m/s2 and show that the maximum speed of the horizontally moving ball clearing the net is about 27 m/s (about 60 mi/h).
c. Does the mass of the ball make a difference? Defend your answer.

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onyebuchinnaji onyebuchinnaji · Answer 1 · 2022-06-08T16:32:41+02:00

(a) The ball’s maximum speed over the net is v(max) = √2gh.

(b) The maximum speed of the horizontally moving ball clearing the net is about 27 m/s.

(c) Speed of the ball is independent of its mass.

The time of motion of the ball is calculated as follows;

h = vt + ¹/₂gt²

1 = 0 + ¹/₂(9.8)t²

1 = 4.9t²

t² = 1/4.9

t² = 0.204

t = 0.452 s

The horizontal speed of the ball is calculated as follows;

X = vt

v = X/t

v = (12 m)/(0.452)

v = 26.6 m/s ≈ 27 m/s (proved)

P.E = K.E

mgh = ¹/₂mv²

gh = ¹/₂v²

2gh = v²

√2gh = v(max)

Speed of the ball is independent of its mass.

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