Answer to Question #300249 in Mechanics | Relativity for Abdullah

Question

A jet-fighter flying borizontally in the direction towards south and at an altitude of 5000 feet with speed 400 mi/h drops a bomb which falls down under the force of gravity. Immediately after releasing the weapon the pilot heads his plane to the northeast direction at a supersonic speed of 700 mi/h (a) what is the time the bomb is in the air" (b) How much horizontal distance does the homb covers during the fall? (c) When the bomb hits the ground, what is the distance between the bomb and the jet.

Answer 1

Explanations & Calculations

a)

• The bomb describes a projectile.
• Apply $‍‍‍‍\small s =ut+1/2at^2$ downward.

$\qquad\qquad \begin{aligned} \small 5000\,ft&=\small 0+\frac{1}{2}(32.17\,fts^{-2})t^2\\ \small t&=\small 17.6\,s \end{aligned}$

• It remains airborne for this time before hitting the ground.

b)

• Neglecting the air resistance, apply $\small s = ut$ horizontally to calculate the range of the projectile.

$\qquad\qquad \begin{aligned} \small s&=\small ut\\ &=\small 400\,mph\times\frac{17.6}{3600}\,h\\ &=\small 1.96\,miles \end{aligned}$

c)

• The distance the jet travels during this time is

$\qquad\qquad \begin{aligned} \small S_j&=\small ut=3.42\,miles \end{aligned}$

• Now you may try drawing a sketch with these dimensions.
• When the bomb hits the ground it will be at the lowest bottom corner and the jet will be at the opposite top corner of an imaginary verticle rectangle. Hence you need to calculate the diagonal length.
• The height of it is 5000 ft and length (L) needs to be calculated with the calculated distances each object travels during the time of 17.6 seconds.
• Try using cosine law to calculate the length of L.