Afootball is thrown horizontally off the top of an apartment house that is 78.4 meters high. the ball is thrownat a speed of 15 m/s. how far will the ball travel

The motion of the ball is a composition of the two motions:
- on the horizontal axis, it is a uniform motion with constant speed 
- on the vertical axis, it is a uniformly accelerated motion with initial speed  and constant acceleration  toward the ground

The laws of motion on the two directions are:


where h=78.4 m is the initial altitude of the ball. 

We want to find how far the ball travels on the x-axis. In order to do that, we must find the time t at which the ball reaches the ground, i.e. the time t at which y(t)=0:



And so now we can find the distance x(t) covered by the ball during this time: