How High Does a Basketball Bounce When Thrown at an Angle?

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The discussion focuses on the physics of a basketball thrown at an angle, specifically analyzing its trajectory and bounce. The acceleration at the highest point is confirmed to be -9.8 m/s² due to gravity. For the bounce, the basketball hits the rim at 3.05 m and bounces up with half the speed it had upon impact. The initial vertical velocity after the bounce is calculated as -1.52 m/s. Further assistance is sought to determine the maximum height the basketball reaches after the bounce.
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An athlete throws a basketball upward from the ground, giving it speed 9.7 m/s at an angle of 64.0° above the horizontal.

(a) What is the acceleration of the basketball at the highest point in its trajectory?
m/s2

(b) On its way down, the basketball hits the rim of the basket, 3.05 m above the floor. It bounces straight up with one-half the speed with which it hit the rim. What height above the floor does the basketball reach on this bounce?

(a) is -9.8m/s2.

For (b) I found the time when the ball hits the rim 1.3s. Then I found the final velocity -3.04m/s and divided by 2 to get -1.52m/s which is the initial velocity of the ball when it bounces straight up vertically from the rim.

I am lost at where to go now and need help with solving (b).
 
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Your time is correct.
Check the calculation of the vertical component of the velocity at that time.
 
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