How many Collisions?

Classical Mechanics Level 4

A smooth spherical ball is dropped vertically on the smooth ground from a height 20 m. Coefficient of restitution of the ground - ball collision is 0.5.

Find the average speed of the ball from its time of drop until it comes to rest

Take g = 10 m/s 2 g = 10 \text{ m/s}^2 .

This is a part of my set Aniket's Mechanics Challenges .


The answer is 5.556.

Aniket Sanghi by Aniket Sanghi , 21, India

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1 solution

Aniket Sanghi
Mar 19, 2016

e is coefficient of restitution

Distance forms series as h + 2 e 2 e^2 h + 2 e 4 e^4 h + .............infinite terms

And time forms series as t +2 et + 2 e 2 e^2 t...........infinite terms...

And average speed is equal to total distance upon total time taken

2 Helpful 0 Interesting 0 Brilliant 0 Confused

1.) What's that "e"??? - Euler's number? Don't believe it!

2.) Thought average speed should be determined from ball's time of drop and NOT from the start!

=> W R O N G!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Andreas Wendler - 4 years, 10 months ago

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e is coefficient of restitution

Aniket Sanghi - 4 years, 10 months ago

e is very easy to understand....where from does euler no. come into existence here...and pls explain what is wrong...since I can't find any blunder.

rajdeep brahma - 3 years ago

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