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A ball is launched from the ground at a 45 degree angle above the horizontal (which we take to be the x-axis). It rises to a maximum height, falls back down to the ground and bounces. After the bounce its velocity again makes a 45◦ angle to the horizontal x-axis, but the magnitude of the velocity right after the bounce is a factor of 3 times the magnitude before the bounce.
Letting the time of the launch be t = 0, the bounce occurs at t = T. After the bounce the ball rises to a new maximum height and then bounces a second time. You can ignore air resistance. Take the acceleration of gravity to be g.

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