Projectile Motion, Find initial velocity knowing x & y dist and time.

[d3nat]

Homework Statement

A football player punts the football so that it will have a time of flight = 4.5s and land 45.7m away. The ball leaves the player's foot 1.52 m above ground.

What is initial velocity? (Magnitude and direction)

Homework Equations

x-x_0 = v_0 * cosθ * t
y-y_0 = v_0 * sinθ * t - 1/2 *g*t^2

v_y = v_0 * sinθ - g*t
v_y^2 = (v_0*sinθ)^2 - 2g(y-y_0)

The Attempt at a Solution

I'm stumped. I can do projectile motion questions, but everytime I have to find initial velocity, I never wind up with the correct answer.

All of the above involve knowing the angle.

I thought maybe θ = tan-1(y/x) but that gives me the wrong angle since that's the angle if the ball was thrown to the ground instead of kicked.

I thought maybe finding the max y height (setting v_y = 0) to solve for angle, but that also involves knowing the angle already.

Help?

Any tips on solving initial velocity questions? I always get stumped on these type. Sigh.

 

[d3nat]

AHAH!

I figured it out :)

Two equations, two unknowns. I solved in terms of v_0, then used that to find my angle (64.9 degrees), then substituted that angle into my horizontal distance formula to find the initial velocity = 24m/s

I feel somewhat silly for having such a hard time with this :/