A place kicker must kick the football from a point 34.2 m from the goal and

Question

clear a bar 3.00 m above the ground. The ball leaves the ground with a speed of 20.0 m/s at an angle of 53.0 degrees above the horizontal.
(a) By how much (m) does the ball clear (positive value) or fall short (negative value) of the cross bar? (This is vertical distance above or below the cross bar.)
(b) When it gets to the cross bar, what is the vertical component of the ball's velocity (m/s)? (Is it rising or falling-pay attention to the sign?)

Answer 1

(a) The horizontal velocity component is 20 cos 53 = 12.036 m/s. To travel 34.2 m to the goal post requires 34.2/12.036 = 2.84 seconds. Its height y at that time is
y(t=2.84) = 20*sin53*t - (g/2)t^2
= 5.84 m. That would be 2.84 m above the cross bar.

(2) V(t=2.84) = 20sin53 - g*t = 15.97 - 27.83 = -11.86 m/s. So the football is falling