ATAR Notes: Forum
WACE Stuff => Mathematics => Mathematics/Science/Technology => WACE => Mathematics Specialist => Topic started by: APK911 on October 02, 2017, 10:51:45 pm
-
As a large wheel rolls along the x-axis, the point Q at the center of the wheel will move horizontally. P is a point on the rim of the wheel and initially, i.e, when t=0, point P lies at the origin. Suppose that the forward speed and the radius of the wheel are such that the velocity of P at time t seconds later is v m/s where, v=(1-cos(t))i+sin(t)j. Find the diameter of the wheel.
Sorry, the question is a little long... But in order to find the diameter, would I have to find the position vector at time t, then sub in t as 2pi, and get the magnitude of the vector?
I've also attached a photo of the question and diagram, if that helps...
-
As a large wheel rolls along the x-axis, the point Q at the center of the wheel will move horizontally. P is a point on the rim of the wheel and initially, i.e, when t=0, point P lies at the origin. Suppose that the forward speed and the radius of the wheel are such that the velocity of P at time t seconds later is v m/s where, v=(1-cos(t))i+sin(t)j. Find the diameter of the wheel.
Sorry, the question is a little long... But in order to find the diameter, would I have to find the position vector at time t, then sub in t as 2pi, and get the magnitude of the vector?
I've also attached a photo of the question and diagram, if that helps...
I think you need to find the position vector and then find the maximum value of the vertical component. That way you'll have the highest distance above the x axis that P is, which would give you the diameter. Though I might be wrong
-
Oh, actually that makes sense. Thank you very much!