You\'re flying your 10,000-kg Scooty Puff Pro spaceship at a constant speed of 2

Question

You're flying your 10,000-kg Scooty Puff Pro spaceship at a constant speed of 20km/s in the positive x-direction.

You're flying your 10,000-kg Scooty Puff Pro spaceship at a constant speed of 20 km/s in the positive x -direction. All of the sudden it malfunctions and many of the thrusters are stuck on. The main thruster is stuck on producing a 800 kN force in the positive x -direction. Two of the small maneuvering thrusters are also stuck on, one producing a 100 kN force in a direction 30 degree from the positive y-direction towards the negative x-direction, and the other is producing a 150 kN force in a direction 10 degree from the negative y-direction towards the negative x-direction. After 2 minutes of this the two maneuvering thrusters shut off and the main thruster decreases in magnitude to 200 kN, while still applying the force in the positive x -direction. It takes an additional 6 minutes to Ex the problem and turn all of them off. How far and what direction would you have to travel to get to where you would have been if the malfunction had not occurred.

Explanation / Answer

Constant speed, v = 20*10^3 m/s
Malfunction Time = 2 min + 6 min
t = 2*60 + 6 * 60 = 480 s

Distance travelled = v*t
Distance travelled = 480* 20*10^3 m
Distance travelled = 9.6 * 10^6 m


Now, Net Force in x direction due to thruster -
Fx = 800 * 10^3 N - 100 * 10^3 * sin(30) - 150*10^3 * sin(10)
Fx = 723953 N

ax = Fx/m
ax = 723953/10000 m/s^2
ax = 72.4 m/s^2

Initial Velocity = 20 * 10^3 m/s
t = 2 * 60 s = 120s
S = u*t + 0.5*a*t^2
S = 20 * 10^3 * 120 + 0.5 *72.4*120^2 m
S = 2.92 * 10^6 m

Velocity after 2 min =
V = u + a*t
V = 20*10^3 + 72.4*120 m/s
V = 28688 m/s

Net Force in y direction due to thruster -
Fy = - 100 * 10^3 * cos(30) + 150*10^3 * cos(10)
Fy = 61119 N
ay = Fy/m
ay = 6.11 m/s^2

Initial velocity = 0
t = 2*60 = 120 s
Sy = u*t + 1/2 * a*t^2
Sy = 0 + 0.5 * 6.11 * 120^2
Sy = 43992 m (towards -ve y axis.)

After this -
Net Force on x direction = 200 * 10^3 N
ax = Fx/m
ax = (200 * 10^3 )/10000 m/s^2
ax = 20 m/s^2

Initial Velocity = 28688 m/s
t = 6 * 60 s = 360s
S = u*t + 0.5*a*t^2
S = 28688 * 360 + 0.5 *20*360^2 m
S = 11.62 * 10^6 m

Total Distance travelled in x direction =  2.92 * 10^6 + 11.62 * 10^6
Total Distance travelled in x direction = 14.54 * 10^6 m

Distance Need to Travel to reach original Destination -
In X direction = (14.54 - 9.6) 10^6 = 4.94 * 10^6 m
in Y direction = 43992 m

Net Distance = sqrt((4.94 * 10^6 )^2 + 43992^2) m
Net Distance = 4.94 * 10^6 m
Direction = tan^-1((4.94 * 10^6 )/43992)
Direction = 89.50 west of North or (from + y axis towards -ve x axis).

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