Question

A particle is projected from point $A$ to hit an apple as shown in Fig. The particle is directly aimed at the apple. Show that particle will not hit the apple. Now show that if the string with which the apple is hung is cut at the time of firing the particle, then the particle will hit the apple.

Answer 1

We know that the range is given as:

$H_1=\frac{u^2{\sin }^2{30}^{\circ }}{2g}=\frac{u^2}{8g}$

$H_2=\frac{u^2{\sin }^2{60}^{\circ }}{2g}=\frac{3u^2}{8g}$

Clearly, $H_2=3H_1$
Sum of angles $=60+30={90}^{\circ }$, the horizontal range is same.