To determine the speed of the combined spaceship after the collision, you can use the principle of conservation of momentum.

Before the collision, the total momentum of the system is the sum of the momenta of Spaceship 1 and Spaceship 2.

Calculate the initial momentum of each spaceship:

Spaceship 1:

Mass

𝑚

300

=300 kg

Speed

𝑣

=0 m/s

Momentum

𝑝

𝑚

⋅

𝑣

300

⋅

⋅v

=300⋅0=0 kg·m/s

Spaceship 2:

Mass

𝑚

300

=300 kg

Speed

𝑣

=4 m/s

Momentum

𝑝

𝑚

⋅

𝑣

300

⋅

1200

⋅v

=300⋅4=1200 kg·m/s

Total initial momentum:

𝑝

total initial

𝑝

1200

\cdotp

m/s

total initial

=0+1200=1200 kg\cdotpm/s

After the collision, the two spaceships stick together, so their combined mass is:

Total mass

𝑀

𝑚

300

600

M=m

=300+300=600 kg

Let

𝑣

𝑓

be the final velocity of the combined spaceship.

The total momentum after the collision must be equal to the total momentum before the collision (conservation of momentum):

𝑝

total final

𝑀

⋅

𝑣

𝑓

total final

=M⋅v

Set this equal to the total initial momentum:

1200

600

⋅

𝑣

𝑓

1200=600⋅v

Solve for

𝑣

𝑓

𝑣

𝑓

1200

600

m/s

600

1200

=2 m/s

So, the speed of the combined spaceship after the collision is

2 m/s.

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