Question

You are stuck on Planet Blitzen (mass of 2x1023 kg and radius of 8x105m). You build a rocket and are trying to determine if you will manage to escape without falling back to the surface. The greatest velocity you can achieve is 6x10^m/. Will this velocity allow you to escape Planet Blitzen? Justify your answer.

Answer 1

You will manage to escape without falling back to the surface.

Step-by-step explanation:

To determine if you can escape Planet Blitzen, we need to calculate the escape velocity using the formula:

v = sqrt((2 * G * M) / R),

where G is the gravitational constant (6.67 x 10^-11 N m²/kg²), M is the mass of the planet, and R is the radius of the planet.

Plugging in the values for Planet Blitzen (mass = 2x10^23 kg, radius = 8x10^5 m), we get:

v = sqrt((2 * 6.67 x 10^-11 N m²/kg² * 2x10^23 kg) / (8x10^5 m))

Simplifying the equation, the escape velocity is approximately 2.4 x 10^3 m/s.

Since your greatest velocity with the rocket is 6 x 10^3 m/s, which is greater than the escape velocity of Planet Blitzen, you will manage to escape without falling back to the surface.