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The merry-go-round rotates counterclockwise with a constant angular speed u. The distance between the horse on...

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Advance Math

The merry-go-round rotates counterclockwise with a constantangular speed u. The distance between the horse on themerry-go-round and the rotational center is r.

(a) Find the position of the horse x and its velocity v, v(t) =d/dt x(t), as vector-functions of time.


(b) Find the acceleration of the horse, a(t) = d^2/dt^2 x(t), as avector-function of time. What is its direction (in comparison withthe direction of x)?

Now the same horse has a non-constant angular speed u(t) (themerry-go- round still rotates counterclockwise).

(c) Find the position of the horse x and its velocity v, v(t) =d/dt x(t), as functions of time.


(d) Find the acceleration of the horse, a(t) = d^2/dt^2 x(t), as afunction of time.

(e) What is the direction of a(t) at the moment when themerry-go-round starts to rotate?

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