Question

A ball is kicked with an initial velocity of 20 m/s in the horizontal direction and 11 m/s in the vertical direction. (Assume the ball is kicked from the ground.) At what speed (in m/s) does the ball hit the ground?

Answer #1

Gravitational acceleration = g = -9.81 m/s^{2}

Initial horizontal velocity of the ball = V_{x0} = 20
m/s

Initial vertical velocity of the ball = V_{y0} = 11
m/s

Time taken by the ball to hit the ground = T

The ball is kicked from the ground therefore the displacement of the ball in the vertical direction is zero when the ball hits the ground.

0 = V_{y0}T + gT^{2}/2

0 = (11)T + (-9.81)T^{2}/2

T = 2.243 sec

Vertical velocity of the ball when it hits the ground =
V_{y1}

V_{y1} = V_{y0} + gT

V_{y1} = 11 + (-9.81)(2.243)

V_{y1} = -11 m/s

Horizontal velocity of the ball when it hits the ground =
V_{x1}

There is no horizontal force acting on the ball therefore the horizontal velocity of the ball remains constant.

V_{x1} = V_{x0} = 20 m/s

Speed of the ball when it hits the ground = V_{1}

V_{1} = 22.83 m/s

Speed of the ball when it hits the ground = 22.83 m/s

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