To win the game, a place kicker must kick a football from a point 45 m (49.212 y

Question

To win the game, a place kicker must kick a
football from a point 45 m (49.212 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 24 m/s at
an angle of 32.6? from the horizontal.
The acceleration of gravity is 9.8 m/s2 .
By how much vertical distance does the ball
clear the crossbar? Answer in units of m.

This problem has been giving me problems since i don't even knowwere to start. What i tried doing was finding the time at the ballshighest moment in flight and then tried doing the horizontaldistance but its asking for the vertical and hence i got it wrong.Please help >.<

Explanation / Answer

   Vertical component ofvelocity   uy   =   u* sin    =   24 * sin32.60   =   12.93   m/s    Horizontal component ofvelocity   ux   =   u* cos   =   20.22   m/s    Time taken by ball to reach thecrossbar   t   =   horizontaldistance / horizontal component of velocity    t   =   45 /20.22   =   2.22   s    i.e. after 2.22 s, the ball will clear thecrossbar. In the same time, suppose the ball rises to a height'h'.    then by second equation of motion    h   =   uy* t   +   (1/2) * g *t2    Since ball is movingupwards,   g   =   -9.8   m/s2    =>   h   =   12.93* 2.22   +   0.5 * ( - 9.8) *2.222   =   4.55   m    Height by which the ball clears thecrossbar   =   h - height ofcrossbar   =   4.5 -3.05   =   1.50   m    =>   h   =   12.93* 2.22   +   0.5 * ( - 9.8) *2.222   =   4.55   m    Height by which the ball clears thecrossbar   =   h - height ofcrossbar   =   4.5 -3.05   =   1.50   m

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