Question

A man in a hot-air balloon drops an apple at height of 150m. If the said balloon is

rising at 15m/s, find the highest point reached by the apple.

Answer 1

Let's write the kinematic equation for the vertical displacement of the apple:

$$y=y_0+v_0t-\dfrac{1}{2}gt^2,$$ $$y=150+15t-4.9t^2.$$

The highest point reached by the apple will be when $\dfrac{dy}{dt}=0$:

$$15-9.8t=0,$$ $$t=\dfrac{15\ \dfrac{m}{s}}{9.8\ \dfrac{m}{s^2}}=1.53\ s.$$

Substituting $t$ into the previous equation we can find the highest point reached by the apple:

$$y=150\ m+15\ \dfrac{m}{s}\cdot1.53\ s-0.5\cdot9.8\ \dfrac{m}{s^2}\cdot(1.53\ s)^2=161.5\ m.$$