# hitting a pool ball at exactly 90 degrees

So a friend and I had an argument and I thought I might get some unbiased proof here. Is it possible to hit a pool ball with another pool ball at exactly 90 degrees. Ie if I had a white ball could I hit another ball to go exactly in a perpendicular direction to the white ball?

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Yes and no. You'd have to hit exactly tangentially and the resulting speed would be exactly zero. (I assume you mean perpendicular to the original direction o fth ewhite ball) –  Hagen von Eitzen Dec 29 '13 at 21:57
But would it impact. Imo it would not impact. Ie if it were to hit it was by definition not tangential ( –  Murdock Dec 29 '13 at 22:00
And yes. Thats what I meant –  Murdock Dec 29 '13 at 22:00
Its more a theoretical question. I would argue that 89.99999... degrees is possible but not 90 degrees –  Murdock Dec 29 '13 at 22:08
Just use a masse shot to curve the ball, that will work –  Asimov Sep 6 at 15:41

Unless the ball you strike is able (or allowed) to change direction before it hits the second ball, (i.e. by bouncing off a cushion) the answer is no. This is due to conservation of momentum and energy. Consider the white ball of mass $m_w$ travelling along a horizontal plane with velocity $v$. The second ball, with mass $m_s$ is initially stationary, so has velocity 0. If the second ball were travelling at right angles to the white ball after impact with velocity $w$, by conservation of momentum, the momentum of the white ball is now $m_w*v-m_s*w$, and for the second ball it is $m_s*w$. But here you have created energy from nowhere - the total kinetic energy of the balls is now greater after the impact than it was before the impact, a contradiction.

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What is the reasoning behind the eqaution for the ne momentum of the white ball and why does this not apply to other angles that is valid? –  Murdock Dec 29 '13 at 22:33
Ok ignore the above comment. I understand how you get the white ball and second balls momentum but do not understand how you conclude that the total kinetic energy is more? –  Murdock Dec 29 '13 at 22:44
@Murdock Say the white ball starts moving noth and the other ball is caused to move west. Then the white ball must still have the same northbound speed plus some eastbound speed. Hnece the white ball is faster after the impact, i.e. has more energy than it had before (when it was the only bearer of kinetic energy). - Interestingly, Edward's argument does not even require the two balls to have the same mass. –  Hagen von Eitzen Dec 29 '13 at 22:56
Ah got it. Makes complete sense thanks guys. –  Murdock Dec 29 '13 at 23:00