# Homework Help: Errors and approximation question

1. Aug 21, 2010

### gkraju

1. The problem statement, all variables and given/known data

In an inertial navigation system on switching ON an intial error of 0.0001m/s^-2 exists in one direction.
After 30 minutes an additional error of -0.00005m/s^-2 in acceleration builds up.
The system navigates for 2hrs 30 minutes after switching ON. compute the error in velocity and distance after every 30 minutes for this navigation

2. Aug 21, 2010

### lanedance

do you have any ideas?

3. Aug 22, 2010

### HallsofIvy

What do you mean by this? Do you mean that there is an intial error of 0.0001 and then after 30 minutes the error becomes 0.0001- 0.00005= 0.00009? And what do you mean by "in one direction"? In what direction? Or is it to be assumed that all motion is in one direction?

Assuming what I have said above, after the first 30 minutes, the acceleration is a+ .0001 so the velocity will be 30(60)(a+ .0001)= 1800a+ 1.8 so there is an error of 1.8 m/s in the velocity. The distance traveled is 30(180)(1800a+ 1.8)= 3240000a+ 32400 so there is an error of 32400 m in distance traveled.

For the next 30 minutes, the acceleration is a+ 0.00009[/math] so the velocity after 30 minutes has changed by 30(60)(a+ 0.00009)= 1800a+ .162. The total velocity would be 1800a+ 1.8+ 1800a+ .162= 3600a+ 1.962. The error in the velocity is now 1.962 m/s. At that velocity, in 30 minutes, the distance traveled is 30(60)(3600a+ 1.962)= 6480000a+ 3531.6[/itex]. The error is distance traveled, after the first hour is 3531.6 m.

For every succeeding 30 minutes, the acceleration error remains 0.00009 so every 30 minutes the error in velocity increases by 30(60(.00009)= .162 m/s and the error in distance traveled increases by 30(60)(.162)= 291.6 m.