It is 2014 and space cadets are training at the World Ceres, where gravity is ne

Question

It is 2014 and space cadets are training at the World Ceres, where gravity is negligable. They use a coordinate system with orgin at Ceres surface, y axis up. Today, Carmen is correctly is executing  a series of maneuvers. At t=0, 3 minutes after maneuver 5 ends, she is crossing the y axis, 20km up from the surface, moving with vz-400m/s, and she begins the 6th manuever, which consists of 40s of constant accelertation, to be followed (after 90s of no acceleration) by manuever 7. At t=30s her velocity is 500m/s in a direction of 36.9 angle from negative z toward positive y.

1. Find her veolcity at t= 2 minutes

2. Find her position component at t=20s

3. Find her position at t= 2minutes

Explanation / Answer

Her inital velocity is (0,0,-400) m/s (now to be noted v(0))

Her initial position is (0,20000,0) m (now to be noted x(0))

At t=30s, her velocity is (0, (500sin(36.9)), -(500cos(36.9)) m/s

which is (0,300,-400) m/s

Change in velocity in 30s is (0,300,0) m/s

Dividing this by change in time of 30s,

acceleration over this time is (0,10,0) m/s^2

This acceleration continued for 10 more seconds.

Then final velocity at t=30s would be (0,400,-400)

Since her velocity does not change afterward as acceleration becomes 0,

answer to part a is (0,400,-400)

b.

Use the formula

x = x(o) + v(o)t + (1/2)at^2

   = (0,20000,0) + (0,0,-400)(20) + (1/2)(0,10,0)(20^2)

   = (0,22000,-8000) m

c.

Calculate it as two segments

Change in position during first 40s.

dx1 = v(0)t + (1/2)at^2

     = (0,0,-400)(40) + (1/2)(0,10,0)(40^2)

     = (0,8000,-16000) m

Change in position during next 80 seconds

dx2 = v(0)t + (1/2)at^2

      = (0,400,-400)(80) + (1/2)(0)(80^2)

      = (0,12000,-32000) m

Final position

= x(0) + dx1 + dx2

= (0,20000,0) + (0,8000,-16000) + (0,12000,-32000)

= (0,40000,-48000) m

Summary

1. (0,400,-400) m/s

2. (0,22000,-8000) m

3. (0,40000,-48000) m

In case you are not familiar with this way of denoting position, veloicty, and acceleration,

First, second, and third values indicate x, y, and z values respectively.

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