Please help me with this math problem?!?

Question

pleaseee help me answer this question! i'm stuck and my finals are tomorrow. i don't need an answer really, i just need someone to explain how to solve the problem

when twinkle toes tony kicked a football, it landed 100 feet from where he kicked it. it also reached a height of 125 feet. write an equation that when graphed will model the path of the ball from the moment it is kicked until it first bounces on the ground.

Answer 1

Step 1: Model the height vs the acceleration due to gravity.
h = vt + 1/2at^2
a = -9.8, so:
h = vt - 4.9t^2

Step 2: Use Torricelli's equation to find the initial velocity irrespective of time:
Vf^2 = Vi^2 + 2ad

At the top of the arc, the velocity is 0. At that point:
Vi^2 = -2ad

Step 3: Given vi and a, find the total time. h = 0 because the ball lands at the end.
h = vit + 1/2at^2
vit = 1/2at^2
vi = 1/2at
t = vi / 1/2a

Step 4: Given t, you can now model the horizontal motion as a straight function where x = vt.