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The average velocity of a particle projected from the ground with speed u at an angle $α$ with the horizontal over a time interval from beginning till it strikes the ground again is $u \cos α$ . What is the change in velocity?

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$(- 2 u \cos α) \hat{j}$

$(- u \cos α) \hat{j}$

$(- u \sin α) \hat{j}$

$(- 2 u \sin α) \hat{j}$

answer is C.

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Detailed Solution

$Δ v = v_{f} - v_{i}$

$= (u \cos α \hat{i} - u \sin α \hat{j}) - (u \cos α \hat{i} + u \sin α \hat{j}) = (- 2 u \sin α) \hat{j}$

Therefore, change in velocity is 2 u $\sin α$ in downward direction.

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