Two particles of different mass, m 2 > m 1 , collide totally inelastically. They

Question

Two particles of different mass, m2 > m1, collide totally inelastically. They initially have identical speeds, however, the direction is at an angle above and below the x-axis, respectively, as shown. Which one of the indicated final velocities is correct?
A, along the initial velocity of particle 2.
B, between the direction of the initial velocity of particle 2 and the x-axis.
C, along the x-axis
D, between the x-axis and the direction of the initial velocity of particle 1.
E, along the initial velocity of particle 1.

If the initial speeds are v1=v2=7.4 m/s and the angle is 49 degrees, what is the x-component of the final velocity
?

Explanation / Answer

initial momentum

Pi = m1*V1 + m2*V2

v1 = u*costhetai - u*sinthetaj

v2 = u*costhetai + u*sinthetaj

Pi = (m1 + m2)*u*costheta i + (m2 - m1)*u*sintheta j

Pf = (m1+m2)*V

Pf = Pi

V = (m1 + m2)*u*costheta i + (m2 - m1)*u*sintheta j / (m1+m2)

V = u*costheta i + (((m2 - m1)/(m1+m2))*u*sintheta)j

V = Vxi + Vyj

m2 < m1

m2 - m1 is negative

(m2-m1) is not equal to m1+m2

the final angle = tan^-1(vy/vx)

angle = tan^-1((m2-m1)/(m1+m2)) < 45 degrees

direction D <--answer

vx = u*costheta = 7.4*cos49 = 4.85 m/s

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