Question

An athlete kicks a ball at an angle of 45° and with a speed that gives it a range of 60 m. The ball takes 2.8 s to land. If the athlete kicks another ball with the same speed, but at an angle between 45° and 55°, which of the following must occur the second time compared to the first time?

Answer 1

So,

$t=\frac{2v_0\sin\alpha}{g}\to v_0=\frac{gt}{2\sin\alpha}=\frac{9.8\cdot 2.8}{2\sin45°}=19.4(m/s)$

Assume that $\alpha=55°$ . We get

$t=\frac{2v_0\sin\alpha}{g}=\frac{2\cdot 19.4\cdot\sin55°}{9.8}=3.24(s)$

$l=\frac{v_0^2\sin(2\alpha)}{g}=\frac{19.4^2\cdot\sin(2\cdot55°)}{9.8}=36(m)$

If the athlete kicks another ball with the same speed, but at an angle between 45° and 55° then the flight time will increase and the flight range will decrease.