An unstable nucleus of mass 2.4 x 10^-26 kg, initially at rest at the origin of

Question

An unstable nucleus of mass 2.4 x 10^-26 kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. One particle, having a mass of m1 = 5.1 x 10^-27 kg, moves in the positive y-direction with speed v1 = 7.0 x 10^6 m/s. Another particle, of mass m2 = 1.5 x 10^-26 kg, moves in the positive x-direction with speed v2 = 3.4 x 10^6 m/s. Find the magnitude and direction of the velocity of the third particle.

magnitude (m/s)
direction (° counter-clockwise from the +x-axis)

Explanation / Answer

mass of 3rd object=2.4 x 10^-26 kg-5.1 x 10^-27 kg-1.5 x 10^-26kg=3.9x10^-27

 

conservation of momentum
in x direction

0=1.5x10^-26x3.4x10^6+3.9x10^-27xv
so vx=-13.07x10^6i m/s

and in y direction

0=5.1 x 10^-27 kgx7.0 x 10^6+3.9x10^-27xv

vy=-9.15x10^6m/s

so magnitude is-13.07x10^6i m/s-9.15x10^6 jm/s is 15.95 x10^6 and

direction

215degree in anti clock

 

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