A ball is projected with velocity v₀ and at an angle of projection α. After what time is the ball moving at right angles to the initial direction?
Select all that apply

Question

A ball is projected with velocity v₀ and at an angle of projection α. After what time is the ball moving at right angles to the initial direction?

G1 Physics · Accepted Answer

Initial velocity is u⃗ = v₀(cosα î + sinα ĵ). At time t, v⃗ = v₀cosα î + (v₀sinα - gt)ĵ. For v⃗ ⟂ u⃗, their dot product is zero: v₀² - gv₀t sinα = 0. Thus t = v₀/(g sinα) = (v₀/g)cosecα. Hence option A.