horizontal velocity

Question

During service, a tennis ball is struck at height h = 1.7 m above a tennis court and moves with velocity v₀ = v_0xi. Assume the ball encounters no air resistance, and use a Cartesian coordinate system with the origin located at the ball's initial position.

h = 1.7 m

v_0x = 27 m/s



Calculate the tennis ball’s horizontal velocity, vfx in m/s, when it strikes the court.

How long, tf in seconds, does the tennis ball move before striking the court?

How far horizontally from the service position, xf in meters, does the tennis ball move before striking the court?

Answer 1

It seems from the given information that the ball's initial velocity is all horizontal (v_oy = 0). So using the h_i = 1.7 m, we first calculate how long the ball takes to fall 1.7 m, because the horizontal motion of the ball does not affect its vertical motion. Use h_f = h_i + v_oy t + 1/2gt². with g = -9.8 m/s/s; -1.7 = 0 + 0 - 4.9t²; t = sqrt (1.7/4.9) = 0.59 sec.

During this time the ball is moving horizontally at constant v_0x = 27 m/s, so that is its horizontal velocity when it strikes the court.

We use v_0x = x_f / t to find the horizontal distance the ball travels before hitting the court. x_f = v_0x t; x_f = (27)(0.59) = 15.9 m.