How Fast Must a Quarterback Throw to Achieve a 171 Meter Pass?

[Phoenix838]

Homework Statement

A quarterback claims that he can throw the football a horizontal distance of 171 m. Furthermore, he claims that he can do this by launching the ball at the relatively low angle of 26.2 ° above the horizontal. To evaluate this claim, determine the speed with which this quarterback must throw the ball. Assume that the ball is launched and caught at the same vertical level and that air resistance can be ignored. For comparison a baseball pitcher who can accurately throw a fastball at 45 m/s (100 mph) would be considered exceptional.

Homework Equations

v_x = v_0x + a_xt
v_y = v_0y + a_yt
x = 1/2(v_0x + v_x)t
y = 1/2(v_0y + v_y)t
x=v_0xt + 1/2a_xt²
y=v_0yt + 1/2a_yt²
v_x² = v_0x² + 2a_xx
v_y² = v_0y² + 2a_yy

The Attempt at a Solution

The difficulty that I'm having is it seems like I don't have enough information to solve the problem. I've got the horizontal distance (x) as 171 meters, the horizontal acceleration (a_x) as 0 m/s², the vertical distance (y) as 0 meters and the vertical acceleration (a_y) as -9.80 m/s².

I know all I need is one more variable in order to solve this problem, but I just can't seem to figure out what I'm missing given the information I've got.

 

[rl.bhat]

Using the relevant equations, you can show that the range of the projectile is given by
R = v^2*sin(2θ) /g. Using this formula find v.

 

[Phoenix838]

Using the relevant equations, you can show that the range of the projectile is given by
R = v^2*sin(2θ) /g. Using this formula find v.

Would you mind explaining how you came up with that formula?