Question

a) A bomb initially at rest on a smooth, horizontal surface is exploded into three pieces.  Two pieces fly off at 90o to each other, a 2.0 kg piece at 20 m/s and a 3.0 kg piece at 12 m/s.  The third piece flies off at 30 m/s.
(i) Determine the direction of motion for the third piece. 
(ii) What is its mass?

b) A billiard ball moving vertically with a velocity of 10 m/s strikes two other billiard balls which are stationary. After the collision the first ball has a velocity of 2.0 m/s in the same direction to its original motion and one of the other balls moves with a velocity of 5 m/s at an angle of 60^o to the right of the vertical. Determine the velocity of the third ball if all of the balls have the same mass.

Answer 1

Solution:

(a)

Given,

Let the 3rd mass flies of at an angle as shown in the figure below.

By conservation of momentum,

Total momentum before explosion = Total momentum after explosion.

(i) In horizontal direction, we have,

   .................. (1)

In vertical direction, we have

  

  

...........,.. (2)

From (1) & (2)

  

The 3rd mass will fly off at angle 48 degrees below positive x axis.

(ii) Using (2)

The mass of third piece is 1.79Kg.