A jet plane flying at a height of 200 m with a velocity of 144 kmh-1 drops a bomb on the enemy camp, when it is just flying over the camp. Is it true that the bomb will not hit the camp?

Question

A jet plane flying at a height of 200 m with a velocity of 144 kmh-1 drops a bomb on the enemy camp, when it is just flying over the camp. Is it true that the bomb will not hit the camp?

Accepted Answer

The above statement is true.Vertical height of the jet plane, y=200 mVelocity of the plane = Horizontal velocity of the bomb ux                                   =144 kmh-1We need to convert kmh-1 to ms-1,⇒144 kmh-1=144×10003600 ms-1   ⇒144 kmh-1=40 ms-1⇒                 ux=40 ms-1Here the acceleration of the bomb is equal to the acceleration due to gravity, g=9.8ms-2Thus, the acceleration of the bomb, a=9.8ms-2Vertical height of the jet plane = Vertical distance traveled by the bomb∴ Vertical distance traveled by the bomb =200 m Once the bomb is dropped, it has an initial velocity of 144 kmh-1 in horizontal motion, and it travels a particular distance where its velocity drops to zero. When the horizontal motion stops and velocity becomes zero, then the vertical motion starts. Thus, the initial velocity of the bomb in the vertical motion uy=0We know that S=ut+12at2---(a)S is the distance traveled u is the initial velocityt is the time taken a is the acceleration From (a) we can  write y=uyt+12gt2----(i)Substituting all the values in the equation (i), We get      200=0×t+12×9.8×t2⇒200=12×9.8×t2 ⇒200=4.9×t2 ⇒2004.9=t2 ⇒     t2=40.85 s⇒      t=40.85 s ⇒        t≅6.4 s This is the time taken by the bomb to reach the ground.Now we need to find the horizontal distance traveled by the bomb.Horizontal distance travelled by the bomb =xWhile horizontal motion, it is not under the influence of gravity and thus acceleration due to gravity g=0.From (a) we can writewe can write x=uxt+12gt2----(ii)Substituting all the values in the equation (ii), We get       x=40×6.4+12×0×(6.4)2⇒x=40×6.4+0 ⇒x=256 mIt was mentioned that the bomb is dropped, when it is just flying over the camp. As the plane was flying with a velocity of 144 kmh-1 the bomb follows a parabolic path and will hit the ground about 256 m away from the enemy camp. So we can conclude that the bomb will miss the target.

A jet plane flying at a height of $200 m$ with a velocity of $144 km h^{- 1}$ drops a bomb on the enemy camp, when it is just flying over the camp. Is it true that the bomb will not hit the camp?

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