Driving a spaceship isn't as easy as it looks in the movies. Imagine you're a physics student in the 31st century. You live in a remote space colony where the gravitational force from any stars or planets is negligible. You're on your way home from school, coasting along in your 20,000 kg personal spacecraft at 2.0 km/s when your computer alerts you to the fact that the entrance to your pod is 500 km away along a line 30 degrees from your present heading. You need to make a left turn so that you can enter the pod going straight ahead at 1.0 km/s. You could do this with a series of small rocket burns, but you want to impress the girls in the spacecraft behind you by getting through the entrance with a single rocket burn. You can use small thrusters to quickly rotate your spacecraft to a different orientation before and after the main rocket burn.

A.) You need to determine three things: How to orient your spacecraft for the main rocket burn, the magnitude Fthrust of the rocket burn, and the length of the burn. Use a coordinate system in which you start at the origin and are initially moving along the x-axis. Measure the orientation of your spaceship by the angle it makes with the positive x-axis. Your initial orientation is 0 degrees. You can end the burn before you reach the entrance, but you're not allowed to have the engine on as you pass through the entrance. Mass loss during the burn is negligible.

B.) Calculate your position coordinates every 50 seconds until you reach the entrance, then plot a graph of your trajectory. Be sure to label the position of the entrance.