# Problem 4-21-Projectile - Part 4 - B

A football is placed on a line \(25\; m\) from the goalpost. The placement kicker kicks the ball directly toward the goalpost, giving it a velocity of \(21.0\; m/s\) at an angle of \(47.0^\circ\) above the horizontal. The horizontal bar of the goalpost is \(3.0\; m\) above the field. How far above or below the horizontal bar of the goalpost will the ball travel?

**Accumulated Solution**

\(v_{0_x}= 21 \cos 47 = (21) \cos47 = 14.32 \;m/s \\ v_{0_y}= 21 \sin 47 = (21) \sin47 = 15.36 \;m/s\)

\(v = v_0 + at \\ s = v_0t + (1/2)at^2 \\ v^2 = v_{0^2}+2as\)

Correct

1st equation- \(v, t\) unknown

2nd equation- \(s, t\) unknown

3rd equation- \(v, s\) unknown

So the vertical motion cannot be used yet. We must look at the horizontal motion.

For motion at constant velocity in the \(x\) direction: