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

  1. Step 1: At the highest point, vertical velocity is zero, and speed is purely horizontal: v = u cos α.
  2. Step 2: The acceleration is purely vertical (downward): a_n = g.
  3. 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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