🎉 Announcing Numerade's $26M Series A, led by IDG Capital!Read how Numerade will revolutionize STEM Learning Oh no! Our educators are currently working hard solving this question. In the meantime, our AI Tutor recommends this similar expert step-by-step video covering the same topics. Numerade Educator ### Problem 96 Easy Difficulty # A proton moving with speed$v_{A 1}$in the$+x$-direction makes an elastic, off-center collision with an identical proton originally at rest. After impact, the first proton moves with speed$v_{A 2}$in the firstquadrant at an angle$\alpha$with the$x$-axis, and the second moves with speed$v_{B 2}$in the fourth quadrant at an angle$\beta$with the$x$-axis$(\text { Fig. } 8.13)$. (a) Write the equations expressing conservation of linear momentum in the$x$- and$y$-directions. (b) Square the equationsfrom part$(a)$and add them. (c) Now introduce the fact that the collision is elastic. (d) Prove that$\alpha+\beta=\pi / 2 .$(You have shown that this equation is obeyed in any elastic, off-center collision between objects of equal mass when one object is initially at rest.) ### Answer ##$\alpha+\beta=90^{\circ}=\frac{\pi}{2} \mathrm{rad}\$

#### Topics

Moment, Impulse, and Collisions

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##### Christina K.

Rutgers, The State University of New Jersey

##### Andy C.

University of Michigan - Ann Arbor

##### Marshall S.

University of Washington

Lectures

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### Video Transcript

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Chatrapati Sahujii Maharaj University

#### Topics

Moment, Impulse, and Collisions

##### Christina K.

Rutgers, The State University of New Jersey

##### Andy C.

University of Michigan - Ann Arbor

##### Marshall S.

University of Washington

Lectures

Join Bootcamp