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A person is standing on a truck moving with a constant velocity 15 m/s. The man throws a ball in such a way that it returns to his hand after the truck has moved 60 m. prove that angle of projection as seen from truck is 90 degree

A person is standing on a truck moving with a constant velocity 15 m/s. The man throws a ball in such a way that it returns to his hand after the truck has moved 60 m. prove that angle of projection as seen from truck  is 90 degree

Grade:11

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
7 years ago
Dear student,
Let the angle with wihich the ball is projected be equal to \Theta.
The vertical velocity of the ball would be given by vsin\Theta if v is the velocity with which the ball has been projected.
The horizontal velocity of the ball would be given byvcos\Theta.
Hence, the vertical distance covered by the ball would be given by:
y=vtsin\Theta-\frac{1}{2}gt^{2}
Thus, if the ball has to come back to the truck, we would have: y=0.
Therefore,
t=\frac{2vsin\Theta}{g}
Hence, the total horizontal distance covered by the ball would be given by:
R=\left (vcos\Theta+15 \right )t=\left (vcos\Theta+15 \right )\left ( \frac{2vsin\Theta}{g} \right )=\frac{v^{2}sin2\Theta}{g}+30\frac{vsin\Theta}{g}=60
Thus for maximum range, \Theta=90^{\circ}.
Regards
Sumit

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