An unstable nucleus of mass 1.7 10 26 kg, initially at rest at the origin of a c

Question

An unstable nucleus of mass 1.7 1026 kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. One particle, having a mass of

m1 = 2.6 1027 kg,

moves in the positive y-direction with speed

v1 = 5.4 106 m/s.

Another particle, of mass

m2 = 7.0 1027 kg,

moves in the positive x-direction with speed

v2 = 3.2 106 m/s.

Find the magnitude and direction of the velocity of the third particle. (Assume that the +x-axis is to the right and the +y-axis is up along the page.)

magnitude     
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m/s direction      ° counterclockwise from the +x-axis

Explanation / Answer

M = 1.7*10^-26 kg
M = m1 + m2 + m3
m1 = 2.6*10^-27 kg
m2 = 5.4*10^-27 kg
m3 = 9*10^-27 kg
v1 = 5.4*10^6 j
v2 = 3.2*10^6 i
v3 = ?

From conservation of momentum
initial momentum = final momentum
Mu = m1v1 + m2v2 + m3v3
0 = 2.6*10^-27*5.4*10^6j + 5.4*10^-27*3.2*10^6i + 9*10^-27*v3
v3 = -[2.6*5.4*10^6j + 5.4*3.2*10^6i]/9
v3 = [-1.56j - 1.92i]*10^6 m/s
|v3| = 2.4738*10^6 m/s

Angle from x axis, theta = arctan(-1.56/-1.92) = 219.0938 degree

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