Finding change in altitude, and speed in x direction and y direction

[yazz912]

1. The problem statement, all variables and given/known
A crazed ostrich names rhomboid runs along a mountain path with coordinates given by
r(t) = < e^t, e^-t, sqrt(2) t>

B) what is the change in rhomboids altitude from t=0 to t= 10

C) what is rhomboids speed in x direction when t=4

D) what is rhomboids speed in y direction when t=4

E) find a formula for the total distance traveled by rhomboid from t= 0 to t=4

2. Homework Equations
• integration
•derivatives
3. The Attempt at a Solution

For part b) the first thing I thought to do was to integrate only the z component ( since it's height) and evaluate the integral from 0 to 10? Which I get 50*sqrt(2)

C) for speed in x direction do I take the magnitude of the derivative of e^t then plug t=4?
x'(t) = e^t
||x'(t)|| = e^t
Plug in t=4 I get 54.6

D) I do the same as C) only this time I use the y component ?

 

[haruspex]

For part b) the first thing I thought to do was to integrate only the z component ( since it's height) and evaluate the integral from 0 to 10? Which I get 50*sqrt(2)

Why are you integrating? What kind of beast is the integral of a position with respect to time?

C) for speed in x direction do I take the magnitude of the derivative of e^t then plug t=4?
x'(t) = e^t
||x'(t)|| = e^t
Plug in t=4 I get 54.6

D) I do the same as C) only this time I use the y component ?

Yes and yes.

 

[yazz912]

That's what my group thought that we had to integrate... So how would we find change in altitude then?

 

[Dick]

That's what my group thought that we had to integrate... So how would we find change in altitude then?

Just find the change in the z coordinate betweent t=0 and t=10.

 

[yazz912]

Just find the change in the z coordinate betweent t=0 and t=10.

Just by simply plugging it into the original Z coordinate?

 

[haruspex]

Just by simply plugging it into the original Z coordinate?

Yes.