related rates: rolling wheel

A wheel with radius 2 m rolls at 18 rad/s. How fast is a point on the rim of the wheel rising when the point is pi
/3 radians above the horizontal (and rising)? (Round your answer to one decimal

place.)

Hello, drewbear!

Quote:

A wheel with radius 2 m rolls at 18 rad/s.
How fast is a point on the rim of the wheel rising when the point
is $\tfrac{\pi}{3}$ radians above the horizontal and rising?
(Round your answer to one decimal place.)

Code:

* * * * * P * o * 2 * * * * * θ * * o - - - - * * C * * * * * * * * * *

The parametric equations of point $P$ are: . $\begin{Bmatrix}x &=& 2\cos\theta & [1] \\ y &=& 2\sin\theta & [2] \end{Bmatrix}$

$\text{We want }\,\frac{dy}{dt}\,\text{ when }\theta = \frac{\pi}{3}$

Differentiate [2] with respect to time: . $\frac{dy}{dt} \;=\;2\cos\theta\,\frac{d\theta}{dt}$

We know that: . $\cos\frac{\pi}{3} \,=\,\frac{1}{2},\;\;\frac{d\theta}{dt} \,=\,18$

Therefore: . $\frac{dy}{dt} \;=\;2\left(\tfrac{1}{2}\right)(18) \;=\;18\text{ cm/sec}$

thank you so much Soroban!!! (Clapping)