A body is projected with initial speed u at angle α to the horizontal. What is its radius of curvature at the highest point of its trajectory?
Answer and explanation
Correct answer: C. (u^2 cos^2 α) / g
- Step 1: At the highest point, vertical velocity is zero, and speed is purely horizontal: v = u cos α.
- Step 2: The acceleration is purely vertical (downward): a_n = g.
- Step 3: Radius of curvature R = v^2 / a_n = (u cos α)^2 / g = (u^2 cos^2 α) / g.
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