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Question

An aeroplane is flying in a horizontal direction with a velocity $$600kmh^{-1}$$ at a height of $$1960$$m. When it is vertically above the point  A on the ground, a body is dropped from it. The body strikes the ground at point B. Calculate the distance AB.


A
3.33km
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B
333km
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C
33.3km
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D
3330km
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Solution

The correct option is A $$3.33$$km
When the body is dropped it will have an initial horizontal velocity which is equal to speed of the aeroplane. So the bomb fall and travel forward too.
Initial horizontal velocity $$v_x=600km/hr$$
$$\Rightarrow v_x=600km/hr=600\times \dfrac{5}{18}m/s$$
                                    $$=166.67m/s$$
Initial vertical velocity $$v_y=0$$
Height $$h=1960$$
Time taken to fall $$=t$$
$$\Rightarrow h=v_yt+\dfrac{1}{2}8t^2$$
$$\Rightarrow 1960=0+\dfrac{1}{2}\times 9.8\times t^2$$
$$\Rightarrow 1960=4.9t^2$$
$$\Rightarrow t^2=\dfrac{1960}{4.9}=400$$
$$\Rightarrow t=205$$
In $$20s,$$ the horizontal distance travelled is AB.
$$\Rightarrow AB=v_xt=166.67\times 20=3333.4m$$
Hence, the answer is $$3333.4m.$$

Physics

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