An unstable atomic nucleus of mass 1.58 10-26 kg initially at rest disintegrates into three particles. One of the particles, of mass 5.20 10-27 kg, moves in the y direction with a speed of 6.00 106 m/s. Another particle, of mass 8.44 10-27 kg, moves in the x direction with a speed of 4.00 106 m/s.

(a) Find the velocity of the third particle.
i + j m/s
(b) Find the total kinetic energy increase in the process.
J

a The velocity of the third particle is

b The total kinetic energy increase

Explanation:

To solve this question we are going to be using the concept of conservation of momentum which is mathematically represented as

From the question

        Mass of  unstable atomic nucleus

        Mass of  x-axis particle

        Velocity of x-axis particle

         Mass of  y-axis particle  

            Velocity of y-axis particle  

 Since the initial mass is known we can obtain the mass of the third particle  

 Using the conservation of mass mathematical expression

Using the mathematical expression above for conservation of momentum

The above is the vector solution now to obtain the value in numeric form we evaluate the magnitude of the vector

To obtain the total increase in  kinetic energy which is mathematically represented as

answer a fan shaped mass of sediment deposited at the base of a mountain front do to an abrupt change in stream gradient;