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Found in: Page 291

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# A spaceship of mass 2.0 106 kg is cruising at a speed of 5.0 106 m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 5.0 105 kg, is blown straight backward with a speed of 2.0 106 m/s. A second piece, with mass 8.0 105 kg, continues forward at 1.0 106 m/s. What are the direction and speed of the third piece?

Velocity of the third piece is 14.6106 ms-1 in forward direction.

See the step by step solution

## Step 1. Given information isM = 2 106 kgm1 = 5 105 kgm2 = 5 105 kgm3 = mgvs = 5 106 ms-1v1  = 2  106 ms-1v2 = 1  106 ms-1

We need to find the direction and speed of the third piece .

## Step 2. Using the law of conservation of mass, we will find out the mass of third piece.

The spaceship initially has a mass M = 2 x 106 kg. After the explosion, the spaceship splits into three pieces,

Using conservation of momentum,

M = m1 + m2 + m3

m3 = M - m1 - m2

m3 = (2106 kg) - (5105 kg) - (8105 kg)

m3 = 7105 kg

= 0.7106 kg

## Step 3. When an object splits into sections, the explosion between them is an inelastic collision where momentums is conserved. The objects have the same initial velocity and we will use the law of conservation of momentum to find out the velocity of third piece.

As per law of conservation of momentum

And momentum is expressed as

P = mv

Therefore,

Msvs = m1 (-v1) + m2v2 + m3v3

v1 is taken as negative because it is moving in backward direction.

Putting values,

v3 =

As the value of v3 is positive, it will move in forward direction.