A projectile is projected at 60° above the horizontal. If R_L is the radius of curvature at launch and R_T is the radius of curvature at the highest point, and R_L/R_T = N, find N.
Physics · Circular Motion · relative angular velocity and radius of curvature
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Question

A projectile is projected at 60° above the horizontal. If R_L is the radius of curvature at launch and R_T is the radius of curvature at the highest point, and R_L/R_T = N, find N.

G1 Physics · Accepted Answer

At launch, aₙ = g cos60° = g/2, so R_L = u²/(g/2) = 2u²/g. At the highest point, speed is u cos60° = u/2 and aₙ = g. Thus R_T = (u²/4)/g = u²/(4g). Therefore R_L/R_T = (2u²/g) ÷ (u²/4g) = 8. Hence N = 8.