Suppose you are navigating a spacecraft far from other objects. The mass of the

Question

Suppose you are navigating a spacecraft far from other objects. The mass of the spacecraft is 2.0 104 kg (about 20 tons). The rocket engines are shut off, and you're coasting along with a constant velocity of ‹ 0, 25, 0 › km/s. As you pass the location ‹ 5, 8, 0 › km you briefly fire side thruster rockets, so that your spacecraft experiences a net force of ‹ 3.0 105, 0, 0 › N for 21.5 s. The ejected gases have a mass that is small compared to the mass of the spacecraft. You then continue coasting with the rocket engines turned off. Where are you an hour later? (Think about what approximations or simplifying assumptions you made in your analysis. Also think about the choice of system: what are the surroundings that exert external forces on your system?)

Explanation / Answer

During thrust, the acceleration in the x-direction is
a = F / m = 500000N/2e4kg = 25 m/s²
During thrust, the x-displacement x = ½at² = ½*25m/s²*(21.5s)² = 5778.125 m
and the velocity attained is v = at = 25m/s² * 21.5s = 537.5 m/s

One hour (less 21.5 seconds) later, the additional displacement
X = vt = 537.5m/s * (3600s - 21.5s) = 2048691.25 m
for a TOTAL X-DISPLACEMENT = 2049228.75 m

Meanwhile, the y-displacement was y = 25000m/s * 3600s = 90000 000 m
Then one hour later you are at
(2049228.75, 90000 000) given the initial location, and in meters (not km).

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