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M2 Coefficient of Restitution Question

Can someone explain question 6iii)a and b. The solution given was 1.6e^2 and 1.6e^3 respectively, but I have no idea at all as to where these came from...

Original post by Mathematicus65

Can someone explain question 6iii)a and b. The solution given was 1.6e^2 and 1.6e^3 respectively, but I have no idea at all as to where these came from...

The time between the first bounce and second is

1.6e

The time between the second bounce and third bounce is the time between the first bounce and second bounce decreased by a factor of

e

.

So the time between the second and third is

1.6e \times e

.

The time between the third and fourth is the time between the second and third decreased by a factor of

e

.

So the time between the third and fourth is

(1.6e \times e) \times e

.

OP

Original post by Zacken

The time between the first bounce and second is

1.6e

The time between the second bounce and third bounce is the time between the first bounce and second bounce decreased by a factor of

e

.

So the time between the second and third is

1.6e \times e

.

The time between the third and fourth is the time between the second and third decreased by a factor of

e

.

So the time between the third and fourth is

(1.6e \times e) \times e

.

How do we know the time between the second and third bounce decreases by a factor e though..??

OP

Does anyone else know ..?

Original post by Mathematicus65

Does anyone else know ..?

Vertically:

Using

s=ut+\frac{1}{2}at^2

for consecutive times the ball hits the ground, we have s=0 and so:

0=ut-\frac{1}{2}gt^2

and

t=0

or

t=\frac{2u}{g}

t=0 is the start of the bounce, and the time to next hitting the ground is

t=\frac{2u}{g}

.

I.e

t\propto u

Since u is scaled by a factor of e each time, it follows that t is as well.

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