In basketball, hang is an illusion in which a player seems to weaken the gravita

Question

In basketball, hang is an illusion in which a player seems to weaken the gravitational acceleration while in midair. The illusion depends much on a skilled player's ability to rapidly shift the ball between hands during the flight, but might also be supported by the longer horizontal distance the player travels in the upper part of the jump than in the lower part. If a player jumps with an initial speed of v_0 = 6.90 m/s at an angle of theta_0 = 40.5 degree, what percent of the jump's range does the player spend in the upper half of the jump (between maximum height and half maximum height)? (Consider up and the initial direction of horizontal motion to be the positive directions.)

Explanation / Answer

MAximum height h = (vsin(40.5))^2/2*g = 6.9*0.65/9.8 =1.02 m

Half of max height h' = h/2 = 0.51 m

Time to reach h' = 0.225/vsin(40.5) = 0.51/6.9*0.65 = 0.11 sec

Time to reach max height = vsin(40.5)/g = 6.9*0.65/9.8 = 0.45 s

Time required = 0.45 - 0.11 = 0.34 sec

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