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An unstable nucleus of mass 1.7 ✕ 10−26 kg, initially at rest at the origin of...

An unstable nucleus of mass 1.7 ✕ 10−26 kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. One particle, having a mass of m1 = 1.0 ✕ 10−27 kg, moves in the positive y-direction with speed v1 = 5.4 ✕ 106 m/s. Another particle, of mass m2 = 7.0 ✕ 10−27 kg, moves in the positive x-direction with speed v2 = 3.6 ✕ 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.)

Solutions

Expert Solution

Initially the system is at rest, the initial momentum of the system is zero.

The first particle move in the positive y-direction, the momentum of the first particle is

The second particle move in the positive x-direction, the momentum of the second particle is

The mass of the third particle is

where M is the mass of the unstable nucleus.

Let v3 be the velocity of the third particle, its momentum is

Total final momentum of the system is

Using conservation of momentum

We get

Substituting , , , , we get

The magnitude of the Velocity is

Since both x and y-component of the velocity vector are negative, the velocity points in the third quadrant. The angle that the velocity makes with the positive x-axis is

Since the vector points in the third quadrant

genius_generous answered 9 months ago
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