JEE Main & Advanced Physics Two Dimensional Motion JEE PYQ - Two Dimensional Relative Motion

A ball is thrown from a point with a speed\[{{v}_{0}}\]at an angle of projection\[\theta \]. From the same point and at the same instant, a 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? [AIEEE 2004]

A) Yes, \[60{}^\circ \]

B) Yes,\[30{}^\circ \]

C) No

D) Yes,\[45{}^\circ \]

Correct Answer: A

Solution :

[a] Man will catch the ball if the horizontal component of velocity becomes equal to the constant speed of man i.e.,

\[{{v}_{0}}\cos \theta =\frac{{{v}_{0}}}{2}\]\[\Rightarrow \]\[\cos \theta =\frac{1}{2}\]

\[\Rightarrow \] \[\cos \theta =\cos {{60}^{o}}\]

\[\therefore \] \[\theta ={{60}^{o}}\]