# Projectile motion

1. Jul 18, 2006

### brunch43

ok, so i just had my exam 10 minutes ago and i cant think of anything else except this seemly easy problem that i couldnt get.

a football is kicked on the horizontal plane (ie. y_0 = 0 ) at some angle alpha, it covers a horizontal displacement of 100 ft 2.5 seconds later, find the initial velocity and the angle. i feel so f-ing stupid, but i will greatly appreciate any help given

2. Jul 18, 2006

### Office_Shredder

Staff Emeritus
You know the horizontal velocity. Since the vertical velocity is independent, try figuring out high the football can go if it's to land in 2.5 seconds

3. Jul 18, 2006

### HallsofIvy

Assume the initial speed is v. The initial horizontal speed is $v cos(\alpha)$, the initial vertical speed is $v sin(\alpha)$. The (constant) vertical acceleration is -g and the there is 0 horizontal velocity so the horizontal speed is the constant $vcos(\alpha)$ and the vertical speed is $-gt+ vsin(\alpha)$. Integrating those, the horizontal position is $vcos(\alpha)t$ and the vertical position is $-(g/2)t^2+ vsin(\alpha)t$. Knowing that the horizontal distance covered in 2.5 sec. is 100 feet, gives $2.5v cos(\alpha)= 100$, You also know that the ball went up and back down to 0 in that time: the vertical equation gives $-(g/2)(2.5)^2+ 2.5 vsin(\alpha)= 0$. That gives you two equations to solve for v and $\alpha$