Question

sean is at work spinning on a merry-go-round. since his feet are place at the very edge, his mom is standing 1 foot away, afraid he might fall. sean's distance, d, from his mom is a sinusoidal function of time. suppose that at 1 second, he passes his mom. four seconds later, he passes her again. the diameter of merry-go-round is 8 feet. a) graph D= f(t), where t is time in seconds. label your axes. b) find a possible formula for D = f(t) c) find sean's distance from mom at 1) 2.5 seconds 2) 5.6 seconds d) find the second time that sean's distance from mom is 6 feet.

Answer 1

Let us say the point of origin is at the center of the merry go round and it is rotating at a constant angular velocity

in 3 seconds the merry go round takes a complete rotation. So the angular speed of it is =

The parametric equation of a circle is,

, Let us say that his mother is standing at x' = r+a, y = 0.

at t = 1s Sean is at x= r. y = 0. So the real time T and our assumed time t has relation T -1 = t

, so putting this in the parametric equation we get,

at time t, ,

At any time the length of the radial vector joining him and his mother:

this equals D, putting in all the values we get,

The Real time T and D has a relation

b) Already done in part A, see previous equation.

C)1. putting t = 1.25-1 in the equation we get,

D = 2.87feet

2. When t = 5.6-1s D = 4.70feet

3. D = 6, solving the equation we get,

Putting in n=1 for smallest solution we get

T = 1.49s