A boy throws a ball upwards with velocity v_0 | vedclass

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(D) For the ball to return to the boy's hand,the net displacement of the ball must be zero. This implies that the path of the ball must be a straight

Vedclass · Accepted Answer

$	an^{-1} (0.4)$

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(D) For the ball to return to the boy's hand,the net displacement of the ball must be zero. This implies that the path of the ball must be a straight line relative to the boy.This is possible only if the initial velocity vector and the net acceleration vector are collinear (acting along the same line).Let the initial velocity be $\vec{v}_0$ at an angle $	heta$ with the vertical.The horizontal component of acceleration is $a_x = 4\, m/s^2$ and the vertical component is $a_y = g = 10\, m/s^2$ (downwards).The net acceleration vector $\vec{a}$ makes an angle $\alpha$ with the vertical,where $	an \alpha = \frac{a_x}{a_y} = \frac{4}{10} = 0.4$.Since the initial velocity must be in the same direction as the acceleration for the ball to return to the starting point,the angle $	heta$ with the vertical must be equal to $\alpha$.Therefore,$	heta = 	an^{-1} (0.4)$.

$A$ boy throws a ball upwards with velocity $v_0 = 20\, m/s$. The wind imparts a horizontal acceleration of $4\, m/s^2$ to the ball. The angle $\theta$ from the vertical at which the ball must be thrown so that the ball returns to the boy's hand is $(g = 10\, m/s^2)$

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