Calculating Initial Velocity & Angle of Football Kicked on Horizontal Plane

[brunch43]

ok, so i just had my exam 10 minutes ago and i can't think of anything else except this seemly easy problem that i couldn't 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

 

[Office_Shredder]

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

 

[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