Question

A particle is projected from the ground at an angle $θ$ with the horizontal with an initial speed $u$ . Time after which velocity vector of the projectile is perpendicular to the initial velocity.

Moderate

Solution

Since, $v ⊥ u or v \cdot u = 0$
or $(u + g t) \cdot u = 0$
or $u \cdot u + (g \cdot u) t = 0$
or $u^{2} + g u t \cos (90 ° + θ) = 0$ (Angle between u and g is 90° + $θ$ )
or $u - g t \sin θ = 0$
$∴$ $t = \frac{u}{g \sin θ}$

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