# Ball explosion

monkey89
An object with total mass mtotal = 14.4 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.9 kg moves up and to the left at an angle of θ1 = 22° above the –x axis with a speed of v1 = 26.8 m/s. A second piece with mass m2 = 5.1 kg moves down and to the right an angle of θ2 = 27° to the right of the -y axis at a speed of v2 = 20.9 m/s. The third mass m3 = 4.4kg.

What is the x-component of the velocity of the third piece?

What is the y-component of the velocity of the third piece?

What is the magnitude of the velocity of the center of mass of the pieces after the collision?

Calculate the increase in kinetic energy of the pieces during the explosion.

Any help would be wonderful and greatly appreciated Thank you.

## Answers and Replies

gsal
what have you tried? what's not working for you?

monkey89
Im not sure where to start this problem. Which equation to use.

JHamm
Momentum is going to be conserved, so the momentum of the ball before it explodes is equal to the sum of the momentums of the 3 pieces

monkey89
So m1v1+m2v2+m3v3/m1+m2+m3

JHamm
If the object was initially at rest then its momentum was zero, that means that:
$$m_1v_1 + m_2v_2 + m_3v_3 = 0$$
It also means that the horizontal components of momentum will add to give zero as will the vertical components.

monkey89
I already tried zero and it didnt work. I dont know what else to try.

Mentor
I already tried zero and it didnt work. I dont know what else to try.
Show exactly what you did.

What did you get for the x and y components of the momentum of m1 and m2?

gsal
are you trying to solve a simultaneous system of equations of 2 equations and 2 unknowns?

Because I think that's where the solution is...you need to take that equation given by JHamm and break it down into x and y components, along with the unknown x and y components of the 3rd mass...don't worry about the angle of it, just yet, just get the x and y components of the velocity and THEN you can do a vector sum of those to get the result.

monkey89
My home work is aon a site called smart physics. I can in put an answer and it will tell me if im right or wrong. I put in zero and it didn't work. I dont know which equation to use or how to find which equation to use.

gsal
actually, it's not even two equation two unknowns...it should be one equation one unknown, twice...very simple...why don't you show what you are trying to do?

monkey89
I just tried to input zero with any equation. The reason i did this was because i don't know what to do. So i was just tring to see if any of the answers would be zero. I don't know which equation to use to start these problems

gsal
It is not a matter of guessing an answer, punch it in the site and see if it is right or wrong...you actually need to solve a couple of equations...have you understood this part yet?

You have been told that the sum of the momentum from all 3 pieces was zero before the explosion and will remain zero after the explosion.

The equation you need to work with has been already posted and you were even told that all you have to do is break it down into x-components and y-components and that each equation still equals zero, from where you should be able to come up with an answer...

...this is a lot of explanation...longer that would have taken me to solve the problem.

hope this helps...

SillyNumberYa
gsal; I don't think you did a good job explaining. I too am at a loss on what to do and I have found the velocity of the third particle. What I dont know what to do is how to actually break it down into the x-component and the y-component!!!

JHamm
For the y component you multiply the velocity by the sine of the angle it makes with the x axis, for the x component you multiply the velocity by the cosine of that angle.
In other words the first one is moving at 26.8m/s at an angle of 22 degrees, so...
$$V_1_x = -26.8\cos{22^o}$$
The negative is there because it is moving towards the negative x direction.
$$V_1_y = 26.8\sin{22^o}$$

Last edited:
monkey89
Where did you get -28.6? I tried -28.6cos(22)/26.8= x
This is what you ment right?

JHamm
Sorry, it should read 26.8 not 28.6, I've fixed it now

monkey89
V_1_x = -26.8\cos{22^0}
I tried to do this equation in my calculator -26.8 divided by cos(22^0). Is this what you ment? Im sorry for all the questions im tring to really understand physic.