a ball striking a horizontal plane with a velocity v rebounds with a velocity 256v/625 after 4th collision. the coefficient of restitution is?
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Its wrong
To find the coefficient of restitution, we need to use the formula:
e = (Vf / Vi)
Where:
e is the coefficient of restitution.
Vf is the final velocity after the collision.
Vi is the initial velocity before the collision.
In this case, the velocity after the 4th collision is given as (256v/625). However, we don't know the initial velocity.
To find the initial velocity, we need to consider the nature of the collisions with the horizontal plane. Since the ball rebounds with the same velocity after each collision, it means that the velocity reverses its direction after each bounce.
This indicates that the initial velocity is equal to the final velocity after the previous collision.
So, let's establish the relationship between the velocity after each collision:
1st collision: Vf = Vi
2nd collision: Vf = -Vi
3rd collision: Vf = Vi
4th collision: Vf = -Vi
Now, we can write the equation based on the indicated velocity after the 4th collision:
(256v/625) = -Vi
To find Vi, we can rearrange the equation:
Vi = -(256v/625)
Now, we can substitute the values of Vi and Vf into the coefficient of restitution formula:
e = (Vf / Vi)
e = ((256v/625) / -(256v/625))
Simplifying the expression:
e = -1
Hence, the coefficient of restitution for the ball striking a horizontal plane is -1.
Tysm
(256/625)^1/4 = (16/25)^1/2 = 4/5
They deliberately picked a fraction for which both the numerator and deniminator are perfect fourth roots.
The answer is 4/5. Each bounce gives you 80% of the height of the previous bounce.