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 3.5 104 kg (about 35 tons). The rocket engines are shut off, and you're coasting along with a constant velocity of ‹ 0, 32, 0 › km/s. As you pass the location ‹ 3, 5, 0 › km you briefly fire side thruster rockets, so that your spacecraft experiences a net force of ‹ 3.0 105, 0, 0 › N for 19.5 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

mass o spacecraft=3.5 x10^4 kg

initial speed= (32x10^3 j) m/s

initial position= ri= ( 3i +5j ) km = (3000i + 5000j) m

now acceleration of object= (3.0x10^5 i)/(3.5x10^4)

a= (8.82 i) m/s^2

now the position of object after 19.5 seconds,

r= ri + Vi t + 0.5 a t^2

r= (3000i+5000j) + (32x10^3 j)(19.5) + 0.5(8.82i)(19.5)^2

r=(4677i +629000j)m

after this time , let Vf is the velocity of spaceship

vf= vi + at

Vf= (32000j )+ 8.82i (19.5)

Vf=(32000i +172j) m/s

now the spaceship travels with this constant speed for one hour,

1 hour= 3600 seconds

so the final position rf= r + Vf (3600)

rF= r=(4677i +629000j)m +(32000i +172j) m/s (3600 s)

rF=(115204667i +1248200j) m

rF= (115205i + 1248 j) KM

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