Question:
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?
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?
Updated On: Jul 5, 2022
- Yes, $ 60{}^\circ $
- Yes, $ 30{}^\circ $
- No
- Yes, $ 45{}^\circ $
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The Correct Option is A
Solution and Explanation
Man will catch the ball if the horizontal component of velocity becomes equal to the constant speed of man $ ie $ , $ {{v}_{0}}\cos \theta =\frac{{{v}_{0}}}{2} $
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Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration