Question

A football was kicked so that it traveled 65 yards in 3.0 total seconds. What was the speed

and angle above horizontal that the ball was kicked?

Answer 1

vx = 65 yd/3 sec = 21.7 yd/sec since horizontal speed is constant

vy = g t = (32 / 3) yd/sec^2 * 1.5 sec = 16 yd/sec where 32/3 is the acceleration due to gravity in yds / sec^2 and 1.5 is the time to travel each way in the vertical direction

V = (vx^2 + vy^2)^1/2 = (21.7^2 + 16^2)^1/2 = 27 yd/sec

tan theta = vy/vx = 16 / 21.7 = .737 theta = 36.4 deg

You can check using the range formula:

R = v^2 sin (2 theta) / g = 27^2 * .955 / (32 / 3) = 65.3 yds

The difference from 65 yds may be rounding error.