Question

1. A Douglas C-47 Skytrain cargo plane is flying at 360 km/h at a height of 8.2102m above a planet with similar gravity but without an atmosphere (i.e., no air), when a skydiver accidentally drops his pumpkin (before jumping). 

a) How long does the pumpkin take to hit the ground?

b)How far has the pumpkin travelled horizontally?

Answer 1

(a)

$$y=\dfrac{1}{2}gt^2,$$ $$t=\sqrt{\dfrac{2y}{g}},$$ $$t=\sqrt{\dfrac{2\cdot8.2102\ m}{9.8\ \dfrac{m}{s^2}}}=1.29\ s.$$

(b)

$$x=v_0t,$$ $$x=360\ \dfrac{km}{h}\cdot\dfrac{1000\ m}{1\ km}\cdot\dfrac{1\ h}{3600\ s}\cdot1.29\ s=129\ m.$$