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

The merry-go-round rotates counterclockwise with a constant angular speed u. The distance between the horse on the merry-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 a vector-function of time. What is its direction (in comparison with the direction of x)?

Now the same horse has a non-constant angular speed u(t) (the merry-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 a function of time.

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

Expert Solution

Colby Messinger answered 2 years ago

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