A place kicker must kick a football from a point 32.0 m (= 35.0 yd) from the goa

Question

A place kicker must kick a football from a point 32.0 m (= 35.0 yd) from the goal, and the ball must clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 19.1 m/s at an angle of 57.0o to the horizontal.

By how much does the ball clear the crossbar (if in fact it does)? Enter positive values if the ball clears and negative values if it falls below the crossbar.

What is the vertical velocity of the ball at the time it reaches the crossbar? Enter positive values if it is still rising and negative values if it is falling.

Explanation / Answer

GIVEN DATA
Distance of goal post from the kicker x= 32m
Height of cross bar h=3.05m
Velocity of projection of ball u= 19.1 m/s
Angle of projection = 570
Sin(570)= 0.8386
Cos(570)= 0.5446
Here the path of foot ball is parabola so here we apply the concept of OBLIQUE PROJECTILE. So
Range of foot ball R =U2 sin2/g
=U2 2 sin cos /g
=(19.1)22sin570cos570/9.8
=34m.
Maximum height reached by the ball H=U2sin2 /2g
=13.09m
The foot ball clears the cross bar in a time t= x/(u cos )
=3.076sec
Vertical velocity of the ball at the time it reaches the cross bar is -----------
Vy = U sin –gt
= -14.1275m/sec

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