JEE Main · 2004 · 24 Apr 2004 · Offline · Kinematics

A ball is thrown from a point with a speed

v_{0}

at an angle of projection

θ

. From the same point and at the same instant person starts running with a constant speed

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?

(A)yes, $6 0^{\circ}$ ✓ Correct
(B)yes, $3 0^{\circ}$
(C)no
(D)yes, $4 5^{\circ}$

Answer: (A)

Solution

The runner can take the ball only if he keeps pace with its horizontal motion, so his speed must match the horizontal component of the throw,

v_{0} cos θ

. Setting

v_{0} cos θ = \frac{v _{0}}{2}

gives

cos θ = \frac{1}{2}

, so the ball must be thrown at an angle of

6 0^{\circ}

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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