Question

You blast off from Mars, and you turn off the rockets when you are 3500 km(3.5×10⁶ m) from the center of Mars, well above its thin atmosphere and headed away from the planet. You intend to leave Mars for good, and by the time you get very far away you want to be coasting at a speed of 1800 m/s. Mars has a mass of 6.4×10²³ kg. The mass of your spacecraft is 5000 kg.

a) Determine the magnitude of the momentum of the spacecraft when it is far away.

Answer 1

The magnitude of the momentum of the spacecraft, once it has left Mars and is coasting far away, is calculated using the formula p = mv, resulting in a momentum of 9 × 10^6 kg·m/s.

Step-by-step explanation:

The magnitude of the momentum of a spacecraft when it is far away from Mars can be determined using the formula for momentum, which is p = mv, where p is momentum, m is mass, and v is velocity. In this case, the mass of the spacecraft (m) is 5000 kg and the velocity (v) when it is coasting far away is 1800 m/s.

To find the magnitude of the momentum, simply multiply the mass of the spacecraft by the velocity:

p = (5000 kg) × (1800 m/s) = 9 × 10^6 kg·m/s

Thus, the magnitude of the momentum of the spacecraft when it is far away from Mars is 9 × 10^6 kg·m/s.