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A ball of mass m is projected from a horizontal surface with a speed u at an angle $θ$ with horizontal. Then ( $\hat{i} a n d \hat{j}$ are unit vector along horizontal and vertical)
a) The change in velocity between point of projection and maximum height is $u \sin θ (- \hat{j})$
b) The change in velocity during its flight is $2 u \sin θ (- \hat{j})$
c) Average velocity during its flight is $u \cos θ (\hat{i})$
d) Average velocity during its half of time of flight is $u \cos θ (\hat{i})$
The correct statements from above are

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a and b only

a and d only

a,b,c,d

a, b,c only

answer is D.

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Detailed Solution

For a projectile, horizontal component velocity remains constant.

If the initial velocity is

$u \cos θ \hat{i} + u \sin θ \hat{j}$

Final velocity is

$u \cos θ \hat{i} - u \sin θ \hat{j}$

Therefore, the change in velocity between point of projection and maximum height is $u \sin θ (- \hat{j})$ , because the vertical component becomes zero at the highest point.

The change in velocity during its flight is $2 u \sin θ (- \hat{j})$

Average velocity during its flight is $u \cos θ (\hat{i})$

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