Can you please help me with this question and show formulas. thank you

Question

A soccer ball is kicked horizontally off a 22.0-meter high hill and lands a distance of 35.0 meters from the edge of the hill. Determine the initial horizontal velocity of the soccer ball.

Answer 1

Newton's laws of motion act independently on different axes of motion. So here, in the vertical direction, there is no initial speed and the ball drops 22 m under constant acceleration of g = 9.8 m/s2 towards the ground. While in the horizontal direction there is no acceleration and thus no change in speed. Therefore, in the horizontal direction you got a constant speed movement for 35 m. To calculate this speed you need the time that it takes. To calculated the time, you can use the vertical drop motion as follows:

22 m = (1/2)*g*t^2 = 0.5*9.8*t^2

t = sqrt(22/4.9) = 2.11 s

Therefore, the horizontal movement also took 2.11 s and thus the velocity to move 35 m is

V = 35 m / 2.11 s = 16.5 m/s