Answer to Question #309614 in Mechanics | Relativity for yoyo

Question

The footballer kicked the ball and it was caught by the opposing goalkeeper, 4 metres above the ground. The ball was traveling at 10 m/s^2.Calculate the kinetic energy of the ball just before it was caught.

Answer 1

Solution.

$v_0=10m/s;$

$h=4m;$

$W_k-?;$

$\dfrac{mv_0^2}{2}=mgh_{max}\implies h_{max}=\dfrac{v_0^2}{2g};$

$h_{max}=\dfrac{100}{2\sdot9.81}=5.1m;$

$mgh_{max}=mgh+\dfrac{mv^2}{2}\implies W_k= \dfrac{mv^2}{2}=mgh_{max}-mgh;$

$W_k=m(gh_{max}-gh);$

$W_k=m(9.81\sdot5.1-9.81\sdot4)=10.79mJ;$

Answer: $W_k=10.79m J.$