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?
Gravitational acceleration = g = -9.81 m/s2
Initial horizontal velocity of the ball = Vx0 = 20 m/s
Initial vertical velocity of the ball = Vy0 = 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 = Vy0T + gT2/2
0 = (11)T + (-9.81)T2/2
T = 2.243 sec
Vertical velocity of the ball when it hits the ground = Vy1
Vy1 = Vy0 + gT
Vy1 = 11 + (-9.81)(2.243)
Vy1 = -11 m/s
Horizontal velocity of the ball when it hits the ground = Vx1
There is no horizontal force acting on the ball therefore the horizontal velocity of the ball remains constant.
Vx1 = Vx0 = 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
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