Question

A jet is travelling at a speed of 1200 km/h and drops cargo from a height of 2.5 km above the ground Calculate the time it takes for the cargo to hit the ground and the range it travels

Answer 1

a) Time of flight: 22.6 s

To calculate the time it takes for the cargo to reach the ground, we just consider the vertical motion of the cargo.

The vertical position at time t is given by

`y(t) = h +u_y t - (1)/(2)gt^2`

where

h = 2.5 km = 2500 m is the initial height

`u_y = 0` is the initial vertical velocity of the cargo

g = 9.8 m/s^2 is the acceleration of gravity

The cargo reaches the ground when

`y(t) = 0`

So substituting it into the equation and solving for t, we find the time of flight of the cargo:

`0 = h - (1)/(2)gt^2\\t=\sqrt{(2h)/(g)}=\sqrt{(2(2500))/(9.8)}=22.6 s`

b) 7.5 km

The range travelled by the cargo can be calculated by considering its horizontal motion only. In fact, the horizontal motion is a uniform motion, with constant velocity equal to the initial velocity of the jet:

`v_x = 1200 km/h \cdot (1000 m/km)/(3600 s/h)=333.3 m/s`

So the horizontal distance travelled is

`d=v_x t`

And if we substitute the time of flight,

t = 22.6 s

We find the range of the cargo:

`d=(333.3)(22.6)=7533 m = 7.5 km`