Question

A car tire has a diameter of 3 feet and is revolving at a rate of 45 rpm. At t = 0, a certain point is at height 0. What is the height of the point above the ground after 45 seconds?


Can you lead me into the right direction?

Answer 1

I did.

Answer 2

I am not sure what that means?

Answer 3

http://www.jiskha.com/display.cgi?id=1313012739

I already answered you below. Click on link.

Answer 4

But it leads me back to this same page?

Answer 5

I will do it again

Answer 6

45 rpm = 2 pi radians * 45 /60 = 1.5 pi radians/second

radius = 1.5 ft

axle at 1.5 ft and up and down from there
so

y = 1.5 - 1.5 cos (1.5 pi t)
to make y = 0 at 0

at 45 s
y = 1.5 - 1.5 cos (67.5 pi)
= 2.77 ft

Answer 7

Thank you for trying to help me but that answer does not fit any of the answer choices.

Answer 8

I know 45rpm translates to 3pi/2 radians. I am not sure what formula to use to figure out height.

Answer 9

Dara! You'd have saved yourself a lot of time if you'd posted your answer choices in your first post.

Instead, you made Damon do a lot of needless work.

Answer 10

It really doesn't matter if the answer was posted or not. It was how it was done. I did not want the answer I just wanted to know what formula I could use so I could do it myself.

Answer 11

You know that the solution is sinusoidal about the axle with circular frequency 1.5 pi radians/second

you know that the axle is 1.5 feet off the ground

the rotation is therefore a sinusoidal function up and down 1.5 ft from h = 1.5 ft or
y = 1.5 + (a sin 1.5pi t + b cos 1.5 pi t)
choose a and b so that y = 0 when t = 0
y = 1.5 - cos 1.5 pi t works

perhaps your answer should be in meters not feet ?

Answer 12

I mean y = 1.5 - 1.5 (cos 1.5 pi t)

Answer 13

2.77 ft = .845 meters, perhaps they want meters although they gave feet.

Answer 14

I tried it a different way I converted 45 rpm into seconds then to cycles. I got 12/3 cycles. Do you know how to find th phase shift?

Answer 15

that 1 2/3 cycles not 12

Answer 16

45 cycles/minute = 45 cycles/60 seconds
= .75 cycles/second
after 45 seconds
.75 cycles/second * 45 seconds = 33.75 cycles

Answer 17

I followed this example

A tire has a diameter of 20 inches and is revolving at a rate of 10rpm, at t=0, a certain point is at height 0. What is the height of the point above the ground after 20 seconds?

10rpm means one cycle in 6 seconds. So after 20 seconds it has completed 3 and 1/3 cycles.
Since at t=0 the point is at minimum height, the phase shift is -1/4 cycle. So the angle is 3 1/3 -1/4 = 3 1/12 cycles. The amplitude is A=10 and the baseline is D=10. The height at t=20 is 10 +10sin(pi/6) = 15 inches.
8 months ago

Answer 18

Now the 33 does not matter, that is complete cycles
all that matters is that the wheel turns .75 of a cycle
which would put a point that started at the bottom 1.5 feet off the ground

whoops, I did my cosine in degrees, not radians
y = 1.5 - 1.5 (cos 1.5 pi t)
= 1.5 - 1.5 cos [1.5 pi(45)(180/pi)
= 1.5 - cos (12150 deg)
= 1.5 -0 = 1.5

Answer 19

Your way is easier, but you did the cycles wrong, it should be 33 3/4
If you start at the bottom and go 3/4 of the way around, you end up at axle height.

Answer 20

The phase shift is another way to do my
a sin wt + b cos wt

you can say instead
c sin (wt - phi)

now if you know that at t = 0, csin(wt-phi) = -1.5
then
c = 1.5 and sin (-phi) = -1
then phi must be -pi/2
or a phase shift of 90 degrees
but 90 degrees from the sine is the cosine, so I just used the -cosine. Right off we know -cosine 0 = -1