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