A. man is riding on a flat car traveling with constant speed of 12 m/s. He wishe

Question

A. man is riding on a flat car traveling with constant speed of 12 m/s. He wishes to throw a ball through a stationary hoop (fixed on the ground) 5.0 m above the height of his hand in such a manner that the ball will be moving horizontally as it passes through the hoop. He throws the ball with a speed of m/s with respect to himself. What must be the vertical component of the initial velocity of the ball? How many seconds after he throws the ball will it pass through the hoop? Write the initial velocity of the ball relative to the ground in terms of unit vector notation.

Explanation / Answer

as it moves only horizontally when it reaches hoop, vertical component must be zero, so maximum height = 5m a) so vertical velocity v = sqrt(2gh) = sqrt(2g*5) = 9.89m/s b) time taken to reach hoop = v/g = 9.89/9.8 = 1.01secs c) as net speed = sqrt(136) horizontal speed , Vh= sqrt(136 - 9.89^2) = sqrt(38) = 6.16m/s so initial horizontal velocity relative to ground = 6.16-12 m/s vertical velocity = 9.89m/s net velocity relative to ground = -5.84 i + 9.89j

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