At an instant the velocity of a projectile is u and its inclination to the horizontal is θ. After what time interval will the particle be moving at right angles to its former direction?
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Question

At an instant the velocity of a projectile is u and its inclination to the horizontal is θ. After what time interval will the particle be moving at right angles to its former direction?

G1 Physics · Accepted Answer

Let the initial velocity be u⃗ = u cosθ î + u sinθ ĵ. After time t, v⃗ = u cosθ î + (u sinθ - gt)ĵ. For v⃗ to be perpendicular to the former direction, v⃗·u⃗ = 0. Thus u² - ug t sinθ = 0, giving t = u/(g sinθ), option A.