JEE MAIN - Physics (2004 - No. 73)
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 $${{{v_0}} \over 2}$$ to catch the ball.
Will the person be able to catch the ball? If yes, what should be the angle of projection θ?
No
Yes, $$30^\circ $$
Yes, $$60^\circ $$
Yes, $$45^\circ $$
Uitleg
Yes, the person can catch the ball when horizontal velocity is equal to the horizontal component of ball's velocity, the motion of ball will be only in vertical direction with respect to person for that,
$${{{v_0}} \over 2} = {v_0}\cos \theta \,\,\,\,$$
or $$\cos \theta = {1 \over 2}$$
$$ \Rightarrow \cos \theta = \cos 60^\circ $$
$$ \Rightarrow \theta = 60^\circ $$
$${{{v_0}} \over 2} = {v_0}\cos \theta \,\,\,\,$$
or $$\cos \theta = {1 \over 2}$$
$$ \Rightarrow \cos \theta = \cos 60^\circ $$
$$ \Rightarrow \theta = 60^\circ $$