Question

An airplane is in level flight at a velocity of 300 miles per hour and an altitude of 5000 ft when it drops a bomb. (a) How long does the bomb take to reach the ground? (b) What will the bomb's velocity be on impact?

Answer 1

The initial speed in horizontal direction is $v_{0h} = 300\space miles/h = 134.112\space m/s$. This speed does not change with time. The initial speed in vertical direction is $v_{0v} = 0m/s$. Thus, the distance travelled in vertial direction is

$$h = \dfrac{gt^2}{2}$$

where if $h = 3000ft = 914.4m$ then $t$ is the time of falling. Thus:

$$t = \sqrt{\dfrac{2h}{g}} = \sqrt{\dfrac{2\cdot 914.4}{9.81}} \approx 13.65s$$

The speed of the bomb in the vertical direction after time $t$ will be

$$v_v = gt = 9.81\times 13.65\approx 133.9065\space m/s$$

The total speed

$$v = \sqrt{v_v^2 + v_{0h}^2} = \sqrt{(133.9065)^2 + (134.112)^2} \approx 189.5m/s$$

Answer. $t = 13.65s$, and $v = 189.5 m/s$.