Projectile Motion - What angle should the quarterback throw the football?

[ElleElle]

A quarterback wants to throw a football at 22.0 m/s to a receiver 31.0 m away. At what angle above the horizontal should he throw it? Assume that the receiver catches the ball at the same height that the quarterback releases it.

The answer should be 19.4° but for some reason I just cannot get it!

Please help me with the steps!

I solved for time by using: x = xi + vit + (1/2)at^2
I got t = 1.13s

Then i used x = vt to solve for velocity in the y direction. vy = 27.5 m/s (which does not seem right)

Then cos θ = adj/hyp which gives me a math error :/

 

[tms]

Treat the horizontal and vertical motions of the ball separately. To find the time, find the vertical component of the ball's velocity, and see how long it will take for the ball to reach its maximum height and come back down.

 

[ElleElle]

Treat the horizontal and vertical motions of the ball separately. To find the time, find the vertical component of the ball's velocity, and see how long ti will take for the ball to reach its maximum height and come back down.

What formula would i use for the vertical component? Vf=Vi+at and Δy=Vit+(1/2)at^2 ?

 

[tms]

Which do you think? You know, or can calculate, the initial vertical speed, you know the speed at the maximum height, you know the acceleration, and you want to find the time. Which equation will give you what you want knowing what you know?

 

[Toranc3]

Try this: Find an equation that gives you the time it takes to go up and down. Then find another equation that gives you the time it takes to get there in the horizontal direction. Hint: You are already given what x is. You will have two unknowns with two equations. Solve for target!

Spoiler

Your also going to need a trigonometry identity.