A spaceship of mass 2.1×106 kg is cruising at a speed of 5.8×106 m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 4.6×105 kg, is blown straight backward with a speed of 2.5×106 m/s. A second piece, with mass 7.9×105 kg, continues forward at 1.3×106 m/s.

Part A
What is the speed of the third piece?
Express your answer using two significant figures. m/s

Part B
What is the directionof the third piece?

Straight backward

Explanation:

Given a space ship of mass

M = 2.1 × 10^6 kg

The space ship is moving at

V = 5.8 × 10^6 m/s

This space ship blows into three

The first part is blown backward I.e. in the negative direction

Then, mass of first part and it's velocity is

M1 = 4.6 × 10^5 kg

V1 = -2.5 × 10^6 m/s

The second part continues in forward motion, I.e positive direction

Then, mass of the second part and it's velocity is

M2 = 7.9 × 10^5 kg

V2 = 1.3 × 10^6 m/s

A. What is the speed of the third piece?

So, we need to know the mass of the third part

M1 + M2 + M3 = M

M3 = M-M1-M2

M3 = 2.1 × 10^6 - 4.6 × 10^5 - 7.9 × 10^5

M3 = 8.5 × 10^5 kg

So, applying conservation of momentum

Momentum before explosion = momentum after explosion

MV = M1•V1 + M2•V2 + M3•V3

2.1 × 10^6 × 5.8 × 10^6 = 4.6 × 10^5 × -2.5 × 10^6 + 7.9 × 10^5 × 1.3 × 10^6 + 8.5×10^5•V3

1.218 × 10¹³ = -1.15 × 10¹² + 1.027 × 10¹² + 8.5 × 10^5•V3

1.218 × 10¹³ + 1.15 × 10¹² - 1.027 × 10¹² = 8.5 × 10^5•V3

1.2303 × 10^13 = 8.5 × 10^5 V3

V3 = 1.2303 × 10¹³ / 8.5 × 10^5

V3 = 1.45 × 10^7 m/s

B. The direction is straight forward since the velocity of the part is positive

i just did an experiment like this in my science class. also the answer is yes, it will get separated because they are two opposites meaning if they are opposite they can not attract.

hope this .!