Golf Ball Question: How Far Does It Travel?

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A golf ball is hit at 40 m/s at a 45-degree angle and bounces off the ground at the same angle, losing 75% of its speed with each bounce. The challenge lies in calculating the total distance traveled before the ball stops, as the problem lacks direct values for acceleration or time. The poster attempts to use kinematics equations but struggles with the need for acceleration to find displacement. They consider calculating the displacement for each bounce until the ball's speed reaches zero. A more efficient method or confirmation of their approach is sought for solving the problem.
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Homework Statement



A golf ball is hit from the freeway at a speed of 40 m/s and an angle of 45 degrees. Upon hitting the ground the ball bounces off the ground at the same angle but loses 75% of its speed on each bounce. How far does the ball travel before stopping?

Homework Equations



Kinematics equations

The Attempt at a Solution



First, I tried breaking the problem into components. Then I realized both x- and y- components of velocity are the same. I'm stuck because I can't exactly sub values into the kinematics equations to find displacement, seeing that I'm not given acceleration nor time.

Any sort of help/hint would be greatly appreciated.
 
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If a = -9.8 m/s^2, then I'd be able to calculate dy... so would I have to repeat this calculation until v2 = 0 and add up all the displacements? Or is there an simpler method?
 

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