Question

The pilot of a military cargo plane flying horizontally at 160m/s is 250m above a base camp.The pilot releases a hatch and a box of supplies drops to the ground. A) How long does it take the box to fall? B) how far from the base did the box fall? Hint represent the base with a dot.

Answer 1

Given,

The initial velocity of the box, u=160 m/s

The height at which the plane is flying, h=250 m

The angle at which the box is dropped, θ=0°

A)

The time of flight of a projectile motion when projected with zero launch angle is given by

`t=\sqrt[]{(2H)/(g)}`

Where g is the acceleration due to gravity and g=9.8 m/s²

On substituting the known values in the above equation,

`\begin{gathered} t=\sqrt[]{(2*250)/(9.8)} \\ =7.14\text{ s} \end{gathered}`

Therefore the box falls to the ground in 7.14 seconds.

B)

The range of a projectile is given by,

`R=ut`

On substituting the known values,

`\begin{gathered} R=160*7.14 \\ =1142.4\text{ m} \end{gathered}`

Therefore the box falls to the ground at 1142.4 m away from the base camp.