- #1

rock.freak667

Homework Helper

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## Homework Statement

http://img234.imageshack.us/img234/9536/scan0006hj0.jpg [Broken]

Two identical snooker balls are at rest at the point A and B of a snooker table, where AB+1m. The liunes AB is aparallel to a smooth side of the table and at a distance of 0.4m from that side. The ball A is projected along the table with a speed of [itex]2ms^{-1}[/itex] to hit the side of the table at C. It rebounds and subsequently hits the ball at B. The angles that AC and CB make with the table are [itex]\alpha[/itex] and [itex]\beta[/itex] respectively (see diagram). The coefficient of resititution between the side and a ball is [itex]\frac{1}{4}[/itex]. Resistances may be ignored and the balls may be considered as particles.

(i)Show that [itex]cot\alpha + cot\beta=2.5[/itex] and [itex]tan\alpha=2[/itex]

(ii) Show that the direction of motion of the ball turns through 90 degrees on impact at C

(iii) find the speed of the ball after impact at C.

## Homework Equations

[itex]e=\frac{\delta v}{\delta u}[/itex]

## The Attempt at a Solution

Well here is my work...in pictures because, typing it up would have taken a long time.

http://img233.imageshack.us/img233/2581/scan0006cb8.jpg [Broken]

http://img396.imageshack.us/img396/4219/scan0007wu2.jpg [Broken]

Strangely enough,I had a hard time looking for ways to show that tan[itex]\alpha[/itex]=2

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