A proton, moving with a velocity of vå, collides elastically with another proton

Question

A proton, moving with a velocity of vå, collides elastically with another proton that is initially at rest. Assuming that after the collision the speed of the initially moving proton is 3.00 times the speed of the proton intially at rest, find the following. (a) the speed of each preton after the collision in terms or vi iniialy moving proton 949 nitialy at rest proton 316 (b) the direction of the velodity vectors after the collision (assume that the initially moving proton scatters toward the positive y direction) initialy maving proton nitially at rest proton relative to the +x direction relative to the +x direction

Explanation / Answer

(b) Applying momentum conservation,

m v0 i = m (0.949 v0)(cos(theta)i + sin(theta1)i) + m (0.316 v0) (cos(theta2)i + sin(theta2)j)

0.949 sin(theta1) = - 0.316 sin(theta2)

0.949 cos(theta1) + 0.316 cos(theta2) = 1

x1 = 18.3 deg and x3 = - 71.6 deg

initial moving = 18.3 deg ......Ans

initially at rest = -71.6 deg Or 288.4 deg ....Ans

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