You are flying a rover away from a new planet. Your rover has a mass m = 2 kg. The gravity on this new planet is so small such that it can be neglected (g=0). There is an air resistance F. It is proportional to the rover's velocity v and directed opposite the direction of its motion or given by: F = -3 v. The rover starts from an initial height 5 m and initial speed 10 m/s upward. We want to find the rover's height as a function of time, y(t).
You are flying a rover away from a new planet. Your rover has a mass m = 2 kg. The gravity on this new planet is so small such that it can be neglected (g=0). There is an air resistance F. It is proportional to the rover's velocity v and directed opposite the direction of its motion or given by: F = -3 v. The rover starts from an initial height 5 m and initial speed 10 m/s upward. We want to find the rover's height as a function of time, y(t).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Write down the equation of motion for the rover based on Newton's Law of motion!
The equation will be in the form of homogeneous 2nd order linear diff eq as follows: + p(t) + q(t)y = 0
Find the value of p(t) and q(t)!
Show that the following functions are the solutions! Y = e
From 2 correct functions in point a), write down the general solution in the form of y(t) = c1Y1(t) + c2Y2(t)
Find c; and c, from the initial condition provided above and write down the position of the rover after time t!
-1.5t
y = 1
Transcribed Image Text:You are flying a rover away from a new planet.
Your rover has a mass m = 2 kg.
The gravity on this new planet is so small such that it can be
neglected (g=0).
There is an air resistance F. It is proportional to the rover's
velocity v and directed opposite the direction of its motion or
given by: F = -3 v.
The rover starts from an initial height 5 m and initial speed 10
m/s upward.
We want to find the rover's height as a function of time, y(t).
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