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 α−gR22v20cos2α 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 t−12gt2=v0 sin α×Rv0 cos α−12g(Rv0 cos α)2=R tan α−gR22v20 cos2 α Hence, the correct choice is (c).

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