First slide

Projection Under uniform Acceleration

Question

A ball is projected with a velocity $3 \hat{i} + 4 \hat{j}$ m/s . The time after which its velocity vector is normal to initial velocity vector is (g = 10 m/ $s^{2}$ )

Moderate

A

0.625 s
B

0.4 s
C

0.833 s
D

0.125 s

Solution

when velocity becomes perpendicular to initial velocity horizontal velocity will remain same but vertical velocity changes.Let the velocity is $3 \hat{i} + v \hat{j}$ as they are perpendicular their dot product will be zero.
$(3 \hat{i} + 4 \hat{j}) . (3 \hat{i} + v \hat{j}) = 0 9 + 4 v = 0 \Rightarrow \Rightarrow v = - \frac{9}{4} = 4 - g t g t = 4 + \frac{9}{4} = \frac{25}{4} t = \frac{25}{40} = 0.625$
alternate method v is perpendicular to u after t= $\frac{u}{g \sin θ} = \frac{u^{2}}{g u \sin θ} = \frac{25}{10 \times 4} = 0.625$

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