Question

A place-kicker must kick a football from a point 36.0 m (about 40 yards) from the goal. Half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 24.0 m/s at an angle of 49.0° to the horizontal.

(a) By how much does the ball clear or fall short (vertically) of clearing the crossbar? (Enter a negative answer if it falls short.) m

(b) Does the ball approach the crossbar (and cross above or beneath it) while still rising or while falling?

Answer 1

a)

Initial Horizontal and vertical components of velocities are

V_ox=24Cos49

V_oy=24Sin49

Horizontal distance traveled

X=V_oxt

total flight time is

t=X/V_ox = 36/24Cos49 =2.286 s

From

Y=Y_o+V_oyt-(1/2)gt²

Y=0+(24Sin49)(2.286)-(1/2)(9.81)(2.286)²

Y=15.77 mm

Therfore the ball clears the post by

=15.77-3.05 =12.72 m

b)

The ball clears the post while falling

Since time taken to reach maximum height is less than total flight time

V_fy=V_oy-gt

at maximum height V_fy=0

0=24Sin49-9.81*t

t=1.8463 s

Answer is while falling