Exploding Pumpkin: Solving for Third Fragment's Velocity, Direction, and Mass

[Forerunner546]

Homework Statement

A pumpkin of mass 3.30kg at rest on a smooth frictionless plane, explodes into 3 pieces in the horizontal plane. A .50kg piece flies to the North at 3.2m/s. A 1.4kg piece flies off (SW) at 4.1m/s.

What is the speed, direction and mass of the third piece?

Homework Equations

M1V1o + M2V2o = M1V1f + M2V2f

The Attempt at a Solution

I assumed the piece was 1.4kg as I subtracted the original pumpkins mass by the known fragmentary masses. I used the conservation of momentum to subtract the original pumpkins mass and velocity by the unknown fragment and equaled it to the two known pieces. M1V1o - M3V3f = M1V1f + M2V2f

This yielded -5.2 as a velocity which seems wrong, and I have no idea how to find the direction of the third piece and no angles were included.

 

[phinds]

The FIRST thing you should always do in working on such problems is to draw a force diagram. For unknown forces you estimate at direction and magnitude from the known forces/directions. Do that and present it here and then we can help you work on the problem.

 

[scottdave]

They do give angles, just not in the sense you may be used to. Get a Compass Rose and find direction of North and South West, then figure out what angles these are.

 

[Forerunner546]

Here’s a diagram

 

[haruspex]

This yielded -5.2 as a velocity which seems wrong

Can't tell where you are going wrong if you do not post your working.

 

[SammyS]

Homework Statement

A pumpkin of mass 3.30kg at rest on a smooth frictionless plane, explodes into 3 pieces in the horizontal plane. A .50kg piece flies to the North at 3.2m/s. A 1.4kg piece flies off (SW) at 4.1m/s.

What is the speed, direction and mass of the third piece?

Homework Equations

M1V1o + M2V2o = M1V1f + M2V2f

The Attempt at a Solution

I assumed the piece was 1.4kg as I subtracted the original pumpkins mass by the known fragmentary masses. I used the conservation of momentum to subtract the original pumpkins mass and velocity by the unknown fragment and equaled it to the two known pieces. M1V1o - M3V3f = M1V1f + M2V2f

This yielded -5.2 as a velocity which seems wrong, and I have no idea how to find the direction of the third piece and no angles were included.

Here’s a diagram

Hello @Forerunner546 .

Your equations are vector equations, because momentum is a vector quantity. So is velocity.

What is the initial momentum ?

 

[Forerunner546]

View attachment 234263

Hello @Forerunner546 .

Your equations are vector equations, because momentum is a vector quantity. So is velocity.

What is the initial momentum ?

There is no initial momentum

 

[haruspex]

There is no initial momentum

Right. So write out the momentum conservation equations for two orthogonal directions.

 

[SammyS]

There is no initial momentum

By this I assume that you mean: the initial momentum is zero.

That's correct.

You can also solve this by arranging the momentum vectors in a triangle and using Law of Cosines and/or Law of Sines.