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A ball moving with velocity $1 \hat i \ ms^{-1}$ and collides with a friction less wall, afetr collision the velocity of ball becomes $1/2 \hat j \ ms^{-1}$. Find the coefficient of restitution between wall and ball.

I approached it like:

enter preformatted text here

Now, $$e=cot^2\theta$$ but $\theta$ is not known. So,We equate velocity $$\sqrt{e^2 sin^2\theta+cos^2 \theta}=1/2$$ But this is hard to solve as $\cot^4 \theta$ get's involved. Is there any other method to do this or any easy method to solve these?

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up vote 3 down vote accepted

Feeling silly now. Just equating the component of velocities along the wall: $$1/2 sin\theta=cos\theta$$ we get $$\tan\theta =2$$ so, $$e=1/4$$

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