A ball is thrown from a point with a speed ν0 at an angle of projection θ. From the same point and at the same instant person starts running with a constant speed v₀/2 to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection θ? (a) No (b) Yes, 30° (c) Yes, 60° (d) Yes, 45°

Answer: (c). The person catches the ball if he always stays under it: horizontal speeds must match. v₀cos θ = v₀/2 ⇒ cos θ = 1/2 θ = 60°, so the answer is (c) Yes, 60°.

A ball is thrown from a point with a speed ν0 at an angle of… | JEE Main 2004 (AIEEE)

Q26JEE Main 2004 · AIEEEMedium

Relative Velocity in Two Dimensions

A ball is thrown from a point with a speed ν0 at an angle of projection θ. From the same point and at the same instant person starts running with a constant speed $\frac{v_0}{2}$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection θ?

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Answer: (c)

The person catches the ball if he always stays under it: horizontal speeds must match.
$v_0\cos\theta = \frac{v_0}{2} \Rightarrow \cos\theta = \frac{1}{2}$
$\theta = 60^\circ$ , so the answer is (c) Yes, $60^\circ$ .

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