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

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.