Collision problem/ space station

[lah214]

Homework Statement

A 4.00 x 10^4 kg space station is in orbit at a speed of =5230 m/s with respect to the earth. Then, with an explosive mechanism much like a cannon, it launches a 300 kg satellite straight ahead with a speed of 6500 m/s. How much kinetic energy was gained during this explosion?

Homework Equations

The Attempt at a Solution

I actually know how to do the problem, I'm just not sure if the velocity of the satelite BEFORE the launching should be 0 or 5230. I'm leaning towards 0, but I really don't know. Which should it be?

 

[anathema]

Thank you for your question. In order to accurately calculate the kinetic energy gained during the explosion, we need to consider the velocity of the satellite before and after the launch.

Before the launch, the satellite is already in orbit at a speed of 5230 m/s, so this velocity must be taken into account in the calculation. The final velocity after the launch is 6500 m/s, so the change in velocity is 6500 m/s - 5230 m/s = 1270 m/s.

Using the equation for kinetic energy (KE = 1/2 * m * v^2), we can calculate the kinetic energy gained during the explosion:

KE = 1/2 * 300 kg * (1270 m/s)^2

KE = 241,050,000 J

Therefore, the kinetic energy gained during the explosion is 241,050,000 J.

I hope this helps clarify any confusion. Please let me know if you have any further questions.

 

[ogb p]

As a scientist, it is important to clarify all variables and assumptions before attempting to solve a problem. In this case, it is not explicitly stated whether the satellite is initially at rest or moving at the same velocity as the space station (5230 m/s). Therefore, it is important to first clarify this information before proceeding with the solution.

Assuming that the satellite is initially at rest, the kinetic energy gained during the explosion can be calculated using the equation KE = 1/2mv^2, where m is the mass of the satellite (300 kg) and v is the final velocity of the satellite (6500 m/s). This would result in a kinetic energy of 6.225 x 10^9 Joules.

On the other hand, if the satellite is initially moving at the same velocity as the space station (5230 m/s), the kinetic energy gained would be different. In this case, the initial kinetic energy of the satellite would be 1/2(300 kg)(5230 m/s)^2 = 4.15 x 10^9 Joules. After the explosion, the final kinetic energy would be 1/2(300 kg)(6500 m/s)^2 = 6.225 x 10^9 Joules. Therefore, the kinetic energy gained during the explosion would be 2.075 x 10^9 Joules.

In conclusion, the final answer would depend on the initial velocity of the satellite, which needs to be clarified in the problem. It is important to always clarify all variables and assumptions before attempting to solve a problem in order to ensure accuracy and avoid confusion.