A projectile has horizontal velocity component 20 m/s. At a certain instant its vertical velocity component is zero. Take g = 10 m/s². If its radius of curvature at that instant is N m, find N.
Physics · Circular Motion · relative angular velocity and radius of curvature
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Question

A projectile has horizontal velocity component 20 m/s. At a certain instant its vertical velocity component is zero. Take g = 10 m/s². If its radius of curvature at that instant is N m, find N.

G1 Physics · Accepted Answer

At this instant the projectile is at the highest point because vᵧ = 0. Its speed is therefore v = vₓ = 20 m/s. Gravity is perpendicular to velocity, so aₙ = g = 10 m/s². Hence R = v²/aₙ = 20²/10 = 40 m. Therefore N = 40.