An unstable nucleus of mass 2.9 10-26 kg, initially at rest at the origin of a c

Question

An unstable nucleus of mass 2.9 10-26 kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. One particle, having a mass of m1 = 8.5 10-27 kg, moves in the positive y-direction with speed v1 = 7.2 106 m/s. Another particle, of mass m2 = 1.4 10-26 kg, moves in the positive x-direction with speed v2 = 3.8 106 m/s. Find the magnitude and direction of the velocity of the third particle.

magnitude= ____? m/s

direction= _____ degrees counterclockwise from the +x-axis

Explanation / Answer

as no external force on the system of the unstable nucleus [the distintegration is due to internal force]

thus ,the momentum of the system is conserved.

total mass,M=2.9*10^-26 kg

m1=8.5*10^-27 kg

v1=7.2*10^6 j m/s

m2=1.4*10^-26 kg

v2=3.8*10^6 i m/s

m3=M-(m1+m2)

=6.5*10^-27 kg

=>initial momentum=final momentum of the system

=>(2.9*10^-26)*0=(8.5*10^-27)*(7.2*10^6 j )+(1.4*10^-26)*(3.8*10^6 i)+ (6.5*10^-27 )*v

=>v=-8.18*10^6 i-9.42*10^6 j m/s

=>magnitude=12.48*10^6 m/s

angle =229 degree from the positive x direction in counter clockwise direction

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