A projectile is fired with speed u at angle θ above the horizontal. The time at which its velocity becomes perpendicular to its initial velocity is:
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A projectile is fired with speed u at angle θ above the horizontal. The time at which its velocity becomes perpendicular to its initial velocity is:

G1 Physics · Accepted Answer

Initial velocity: initial velocity vector = u cosθ î + u sinθ ĵ. Velocity at time t: velocity vector = u cosθ î + (u sinθ−gt) ĵ. For perpendicular vectors, initial velocity vector·velocity vector = 0. Thus u²cos²θ + u sinθ(u sinθ−gt)=0 ⇒ u²−ug t sinθ=0. Hence t = u/(g sinθ). This instant lies within the flight only when θ≥45°.