A nine cot long rod attached at cne end A to a point on wheel of rad us 3 feet,

Question

A nine cot long rod attached at cne end A to a point on wheel of rad us 3 feet, centered at th origin. The other end B is free to move back and orth along the x-axis. The paint A is at 3, 0 at tim t 0 and the wheel rotates counterclock lie at 4 sec (a) As the point A makes one complete revelution, indicate in the picture the direction and range of motion of the peint 8 (b) Find the coordinates of the point A as a function of time t. xtt)- yit) (c) Find the coordinates of the point B as a function of time t xtt) yit)- (d) What is the x e of the point 8 when r = 1? You should be able to find this two ways: with your function from part (c), and using some common sense (where is port A after one second?).

Explanation / Answer

a. Solution : The second pictur (right side in first row) is the correct answer.

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b. Solution : Radius = 3,

We know that Angel = angular speed x time

= 4 t rad.

Thus x(t) = 3 cos (4t)

And. y(t) = 3 sin (4t)

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c. Solution : The coordinate of point B,

x(t) = 12 - 3cos (4t)

y(t) = 0.

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d. Solution : As the point A revolve 4 time in one second, thus after 1 second point A will at (3, 0).

Hence x =3.

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