Question

2. A small meteor in space, of mass 25000.0 kg, collides with a satellite of mass 9600.0 kg. Afterwards, the two objects merge into a single object. If the meteor was travelling at a speed 250.0 m/s, and the satellite was travelling at a speed of 375.0 m/s, calculate the new speeds if…a) …they were initially moving TOWARDS each otherb) ….they were initially moving in the same direction.

Answer 1

Given

Mass of the meteor, m=25000.0 kg

Mass of the satellite, m'=9600.0 kg

The speed of the meteor, v=250.0 m/s

The speed of the satellite, v'=375.0 m/s

To find

The speed after the collision

Explanation

Let the combined speed after collision be u.

a) they were initially moving towards each other

Let us consider the right direction to be positive.

Considering the meteor to be travelling towards the right and the satellite towards left.

By conservation of momentum

$\begin{gathered} mv+m^{\prime}v^{\prime}=(m+m^{\prime})u \\ \Rightarrow25000\times250+9600\times(-375)=(25000+9600)u \\ \Rightarrow u=76.58\text{ m/s} \end{gathered}$

The combined speed is 76.58 m/s

b) they are moving in same direction

Let both the meteor and satellite moves towards the right direction

$\begin{gathered} mv+m^{\prime}v^{\prime}=(m+m^{\prime})u \\ \Rightarrow25000\times250+9600\times375=(25000+9600)u \\ \Rightarrow u=284.68\text{ m/s} \end{gathered}$

The combined speed is 284.68 m/s

Conclusion

a. The combined speed is 76.58 m/s

b. The combined speed is 284.68 m/s