# What is the speed of a piece of a spaceship that blew up?

• oneamp
In summary, a spaceship of mass 2.30×106kg is cruising at a speed of 5.50×106m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 5.20×105kg, is blown straight backward with a speed of 2.30×106m/s. A second piece, with mass 8.40×105kg, continues forward at 1.30×106m/s.

## Homework Statement

A spaceship of mass 2.30×106kg is cruising at a speed of 5.50×106m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 5.20×105kg , is blown straight backward with a speed of 2.30×106m/s . A second piece, with mass 8.40×105kg , continues forward at 1.30×106m/s .

## The Attempt at a Solution

Using mv=p, I calculated p of each piece like this:
p1 = 1.196*10^12
p2 = 1.092*10^12
p_total = 1.265*10^13

Then I found p3 by subtracting p2+p1 from p_total.

I divided p3 by the mass of the mystery piece: p/940,000 = 1.0302*10^13

But... the answer was wrong. I also tried subtracting: p1-p2 =pt and working from there. What am I doing wrong?

Thanks

Momentum is a vector. You need to add the three momenta (after explosion) as vectors. Here, in 1D, be careful with the signs. A diagram may help.

But it's not 1D, right? Because one goes forward, one goes back, and the mystery piece I am solving for goes off in an unspecified direction...

I got it, thanks for that tip.

I believe you are right in using the conservation of momentum to tackle this problem. The initial momentum should equal the final momentum of the combined three pieces, such that

pinitial = p1 + p2 + p3

m(total)v = m1v1 + m2v2 + m3v3

p(total) = (2.3x106kg)(5.50 x 106m/s) = (1.265x1013)

p1 = (5.20×105kg)(-2.30×106m/s) = (-1.20x1012)

p2 = (8.40×105kg)(1.30×106m/s) = (1.092x1012)

p3 = (9.4x105kg) v3

Because the first piece was blown backwards, it becomes important to apply the negative to its velocity component, and should look like,

(1.265x1013) = (-1.20x1012) + (1.092x1012) + (9.4x105kg)(v3)

It becomes simple to solve for v3 . I assume the sign was causing your problem in the calculations. The mass of the third piece was found by the missing mass, m(total) = m1 + m2 + m3

Because the problem doesn't specify, i took the assumption that the collision only occurs in a single direction, along the x-axis, and that the velocity of each piece doesn't have to be broken down into individual x- and y-components.

## 1. What is the definition of speed?

Speed is a measure of how fast an object is moving, calculated by dividing the distance traveled by the time it took to travel that distance.

## 2. How is the speed of a piece of a spaceship calculated?

The speed of a piece of a spaceship can be calculated by dividing its distance traveled by the time it took to travel that distance. This can be done using various instruments such as radar guns or GPS devices.

## 3. Can the speed of a piece of a spaceship differ from the speed of the entire spaceship?

Yes, the speed of a piece of a spaceship can differ from the speed of the entire spaceship. This can occur if the piece of the spaceship is moving in a different direction or at a different velocity than the rest of the spaceship.

## 4. How does the speed of a piece of a spaceship that blew up compare to the speed of a piece of a spaceship that did not blow up?

The speed of a piece of a spaceship that blew up can be significantly greater than the speed of a piece of a spaceship that did not blow up. This is because the explosion can provide an additional force and acceleration to the piece of the spaceship, causing it to travel at a higher speed.

## 5. Is the speed of a piece of a spaceship that blew up constant?

No, the speed of a piece of a spaceship that blew up is not constant. It can vary depending on factors such as the force of the explosion, the direction and angle of the explosion, and any external forces acting on the piece of the spaceship. It can also decrease over time due to factors such as air resistance or gravity.