Question

A place kicker must kick a football from a point 34.2 m from a goal. As a result of the kick, the ball must clear the crossbar, which is 3.05 m high. When kicked the ball leaves the ground with a speed of 20.5 m/s at an angle of 53° to the horizontal.

(a) By how much does the ball clear or fall short of clearing the crossbar?
m

Answer 1

Given u = 20.5m/s

= 53

Find Range

Range

R = 20.5² sin106 /9.81

R = 41.18 m

so the ball will clear the horizontal distance

Lets see whether ball clears the height of crossbar

projectile motion can be split into 2 - motion in horizontal direction and motion in vertical direction

Speed = distance /time

Horizontal speed = horizontal distance/time

Ux = 34.2 /t ,Ux=Ucos53

t = 34.2/Ucos53

= 2.77sec

now lets find height at that time

y = Uyt - 1/2gt²

= Usin53t - .5*gt²

= 20.5 sin53 * 2.77 -0.5*9.81*2.77²

y = 7.715 m

clearance height = 7.715 - 3.05 = 4.665m

ANSWER : The ball will clear the crossbar at a height of 4.665m