# Problem 4-21-Projectile - Part 5 - C

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

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

Correct.

Before continuing calculate the time of flight from $x = 0$ to $x = 25\; m$

Accumulated Solution

$v_{0_x}= 21 \cos 47 = (21) \cos47 = 14.32 \;m/s \\ v_{0_y}= 21 \sin 47 = (21) \sin47 = 15.36 \;m/s \\ x = v_{x^t} \\\; t = x/v_x = 25 \;m/14.32 \;m/s = 1.75\; s$

Now return to the vertical motion. Which of the three Galilean equations can be used to find the vertical displacement?

(A) $v = v_0 + at$

(B) $s = v_{0^t} + (1/2)at^2$

(C) $v^2 = v_{0^2} +2as$