A horizontall y moving tennis ball barely clears the net, a distance y above the

Question

A horizontall y 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 to 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=d/?2y/g

B.) Suppose the height of the net is 1.0m, and the court's border is 12.0m from the bottom of the net. Use g=10m/s2 and show that the maximum speed of the horizontally moving ball clearing the net is about 27 m/s

C.) Does the mass of the ball make a difference? Defend your answer.

Explanation / Answer

If the ball is traveling horizontally when it passes the net, then with respect to the vertical direction it is like being dropped from rest, So we need to find the time for a ball to drop vertially from height y to the ground

We know V0 but not final V at the ground. So use the equation of motion without final V.

Disiatnce (y) = V0 * t + (1/2) a * t^2 and a is gravity (g) and V0 = 0 m/s

y = (1/2) a * t^2

solve for t

t = sqrt (2*y/g)

Now to find the horizontal distance (d), it is equal to the horizontal speed (v) times the time of flight (t)

d = v * t

v = d / t

now substitute in our equation for time.

v = d / (sqrt (2*y/g))

b) just plug in the numbers and solve for v.

v = 12 m / (sqrt (2*1 m/10 m/s^2))

v = 26.83 m/s

c) No, if it did, then m would be in the equation. Because the mass doesn't effect the seed of the fall.

Good Luck

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