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?
A) Yes, \[60{}^\circ \]
B) Yes, \[30{}^\circ \]
C) No
D) Yes, \[45{}^\circ \]
Correct Answer: A
Solution :
Key Idea: Man will catch the ball if the horizontal component of velocity becomes equal to the constant speed of man, Horizontal velocity component of ball = constant speed of man i.e., \[{{v}_{0}}\cos \theta =\frac{{{v}_{0}}}{2}\] \[\Rightarrow \] \[\cos \theta =\frac{1}{2}\] \[\Rightarrow \] \[\cos \theta =\cos {{60}^{o}}\] \[\therefore \] \[\theta ={{60}^{o}}\]
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