An object of mass 4 kg moving with a speed of 8 m/s along the positive x-axis sp

Question

An object of mass 4 kg moving with a speed of 8 m/s along the positive x-axis splits up into two pieces, one of the mass 3 kg and another of mass 1 kg. The 3 kg piece is observed to be moving at a speed of 6 m/s at an angle of 30 degrees to the positive x axis. We want to find the speed of the second piece and the angle it makes with the x axis. What would be the best way to solve this problem.

A. Find the impulse provided by the force that broke the originl object and use that to calculate the change in momentum which can then be used to finally find the velocity of the 1 kg piece.

B. Since we know the mass of all the objects we can find the force of gravity on each and use that to find the impulse on each piece. That is then used to find the change in momentum and then the final momentum. From the final momentum we could find the velocity.

C. Treat this moving object as an isolated system. Since it breakes up due to internal forces, the next external force is 0, which implies the net momentum before splitting and after splitting is the same. Since we know the momentum before splitting and of the 3 kg after splitting, we use momentum conservation to find the momentum of the 1 kg piece.

D. We can use the idea that the net velocity before and after splitting should be the same. Since we know the velocity before splitting and of the 3 kg piece after splitting, we can determine the missing velocity of the 1kg piece as 2 m/s at an angle of -30 degrees to the x axis.

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Show how you would use your chosen method to find the velocity of the 1 kg piece.

Explanation / Answer

I will use the method of conservation of linear momentum to find out the velocity and direction of the 1 kg mass.

Along horizontal direction

4 * 8 = 3 * 6 * cos (30) + 1 * Vx

Along verticle

3* 6 * sin (30) = 1 * Vy

Hence Vx = 16.4 m/s

Vy = 9 m/s

Hence the final velocity will be 18.7 at 28.7 degree

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