#### pleasehelpmath

##### New member

- Joined
- Sep 26, 2017

- Messages
- 1

mile due South of the carousel at 1:00 p.m. Consider two coordinate systems

with origin the central point about which the carousel rotates. The rst

system, X = (x1; x2), is stationary and is oriented in the usual East-West,

North-South fashion, but the second system is attached to the carousel, which

is rotating counterclockwise with constant angular speed ! with respect to

X. The rotating system is denoted by Yt = (yt1; yt2), and at 1:00 p.m. t = 0

and Yt = Y0 = X.

(a) Find a matrix O such that X(p)T = OYt(p)T for each point p in space.

**O = (cos(tw) -sin(tw)**

sin(tw) cos(tw))

sin(tw) cos(tw))

(b) Find the position of the train as a function of t as measured by both X

and Yt:

So I know that the train moves along the direction vector (cos(pi), sin(pi))

so... positionx(t) = (0, -2) + tv(1,0) = (tv, -2)

then does positiony(t) = (cos(tw) -sin(tw) (tv

sin(tw) cos(tw)) -2)

So I know that the train moves along the direction vector (cos(pi), sin(pi))

so... positionx(t) = (0, -2) + tv(1,0) = (tv, -2)

then does positiony(t) = (cos(tw) -sin(tw) (tv

sin(tw) cos(tw)) -2)

(c) Find the velocity of the train in both systems.

**I could do this part if I had both positions (stationary and moving one), but not confident in part (b)**

(d) Let Z be a coordinate system attached to the train oriented in the usual

north-south, east-west fashion. Find the relation linking Z coordinates to

those of X:

(d) Which of the three coordinate systems are inertial? Why?

**I know how to determine if X, Y, Z are inertial, but not sure what X, Y, and Z are.**

(e) A bird is spotted at X = (0; 0)

ying with speed u on a course 45o east of

due north as viewed by the stationary observer X: Find its position vector

relative to X;Y; and Z: