A spacecraft of total mass m = 1000 kg (fuel, cargo, astronauts, propellant, etc.) wants to dock with a large space station. The docking hatch faces in the x?direction, so the spacecraft's velocity needs to be only in the x?direction at +0.2 m/s. In symbols, the spacecraft needs to be moving at ?v = (0.2, 0) m/s.)However, the spacecraft is currently moving at ?v = (0.4, 0.3)m/s. Thankfully, it has a maneuvering thruster: a rocket that exhausts gas at ve = 2000 m/s that can be pointed in any direction. The pilot waits until the spacecraft is lined up with the docking hatch, then fires the rocket to correct the spacecraft's velocity.a) Draw at least one cartoon that will help you solve this problem, showing the spacecraft, the station, and the exhausted gas. (5 pointsb) Determine the direction that the pilot needs to point the thruster, and how much gas (in kg) they should use, to make this maneuver. (Note: There is a certain approximation that you might choose to make in this problem. If you make this approximation, call attention to the fact that you have made it, and explain why this approximation doesn't change your result by enough to matter.) (20 points)

A spacecraft of total mass m = 1000 kg (fuel, cargo, astronauts, propellant, etc.) wants to dock with a large space station. The docking hatch faces in the xdirection, so the spacecraft's velocity needs to be only in the xdirection at +0.2 m/s. In symbols, the spacecraft needs to be moving at U: (0.2, 0) m/s.) However, the spacecraft is currently moving at 17 = (0.4,0.3)m/s. Thankfully, it has a maneuvering thruster: a rocket that exhausts gas at Us = 2000 m/s that can be pointed in any direction. The pilot waits until the spacecraft is lined up with the docking hatch, then res the rocket to correct the spacecraft's velocity. a) Draw at least one cartoon that will help you solve this problem, showing the spacecraft, the station, and the exhausted gas. (5 points)