Question

Q1. A hand grenade of total mass 5kg explodes into three pieces. Two of them, each of mass 1kg, have velocities of 8m/s with an angle of 43° between them. What is the speed of the third piece?

**well the answer should be 3.9 m/s as per my HW, I just kept getting It wrong, kindly show how to solve for this answer.

Q2. is similar

a hand grenade has a mass of 6kg and It explodes into 3 pieces each of the same mass. two of them go off, each with a speed of 17 m/s with an angle of 60 degrees between their trajectories. what is the speed of the third?

the answer should be 29.4 (as per my homework) I just don't know how to solve It.

Answer 1

In the explosion the linear momentum remains conserved.

Therefore we can write

                                    

Where, is total momentum before explosion, and is total momentum of the system after the explosion.

Since, it is explosion

                                  

Q1:

The first two pieces has mass of 1 kg and moving with 8 m/s speed by a deviation of 43^o with each other.

Let the third particle is moving with 'v' speed and making an angle of with second piece.

Let the direction of the motion of second piece is along x-axis.

So by using conservation of momentum, we can write

   

              

             

We know that

     

So we have

           or

and    or

dividing both the equations, we get

                    

                  or,  

We have

                   

                or,

                or,

I don't know, why your HW is showing 3.9 m/s. But answer should be 4.96 m/s. You can check the answer by reverse calculation.

Solve the second question with the same procedure.

For any doubt please comment.