A girl kicks a ball at a horizontal speed of 15ms^1 off of a ledge 20m above the ground. What is the horizontal displacement of the ball when it hits the ground?

As we are looking for the horizontal displacement first we look at horizontal motion. We know that the horizontal velocity is 15ms^-1 but we dont know the time so we can't work out the horizontal displacement from this. So we must consider vertical motion to calculate the time taken for the ball to reach the floor as it is equal in horizontal and vertical motion. As the ball is moving at a speed horizontally we know that the initial vertical velocity u=0. We also know that the vertical displacement s=20 and that acceleration due to gravity a=9.8. So of SUVAT we have S, U and A and are trying to find T. So of the SUVAT equations we want to use s=ut+0.5at^2 as it doesn't contain any variables we don't know except for T which we are looking for. Sub in the variables we know (S, U and A) and rearrange to find T. 20=(0)t+(0.5)(9.8)t^2 t=2.02 Now use t as the horizontal time in speed=distance/time to find the horizontal displacement distance=speed x time x=15 x 2.02 = 30.3m