Question

An moving airplane dropped a cargo (ignore the effect of air resistance). If the plane from which the cargo was dropped was flying at a height of 600m, and the cargo lands 300 m horizontally from the initial dropping point,

a. how fast was the plane flying when the bottle was released? (Vix=?)

b. what was the velocity of the bottle right before it hit the ground? (Vfy=?)

Solve for time first using this equation: t=√2y/ay

c. draw a figure or diagram that illustrates the given problem

Answer 1

$$L=v_0\sqrt{2H/g},\quad t=\sqrt{2H/g}$$

(a)

$$v_0=L\sqrt{g/2H}\\ =300*\sqrt{9.8/2*600}=27.1\:\rm m/s$$

(b)

$$v=\sqrt{v_0^2+2gH}\\ =\sqrt{27.1^2+2*9.8*600}=112\:\rm m/s$$

(c)

$$t=\sqrt{2*600/9.8}=11\:\rm s$$