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Question

A cannon on a level plain is aimed at an angle α above the horizontal and a shell is fired with a muzzle velocity v0 towards a vertical cliff at a distance R away. Then the height from the bottom at which the shell strikes the side walls of the cliff is


A

R sin αgR22v20sin2α

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B

R cos αgR22v20cos2α

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C

R tan αgR22v20cos2α

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D

R tan αgR22v20sin2α

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Solution

The correct option is C

R tan αgR22v20cos2α


The time taken to move a horizontal distance R is t=Rv0 cos α.
Therefore, the vertical distance moved in this time is given by
h=v0 sin α t12gt2=v0 sin α×Rv0 cos α12g(Rv0 cos α)2=R tan αgR22v20 cos2 α
Hence, the correct choice is (c).


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