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/s²

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_y0T + gT²/2

0 = (11)T + (-9.81)T²/2

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 = V₁

V₁ = 22.83 m/s

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