The record for a ski jump is 180 m set in 1989. assume the jumper comes off the end of the ski jump horizontally and falls 90 m vertically before contacting the ground . what was the initial horizontal speed of the jumper?

Let's write the equations of motion on both x- (horizontal) and y- (vertical) axis. On the x-axis, it's a uniform motion with constant velocity vx. On the y-axis, it is a uniformly accelerated motion with initial height h=90 m and acceleration of  pointing down (so with a negative sign):



First, let's find the time at which the jumper reaches the ground. This happens when Sy(t)=0:

and so 


Then, we can find the horizontal speed. In fact, we know that at the time t=4.28 s, when the jumper reached the ground, he covered exactly 180 m, so Sx=180 m. Using this into the law of motion in x, we find