1. ## Circular-rectilinear transfer

Hi, I'm Tim for Quebec, Canada and I'm having a hard time grasping the whole problem and how to solve it. I'd appreciate it a lot if you could help me with this one. Thank you very much and best regards.

P.S. I translated the problem from French to English the best I could and I couldn't find a proper way to translate part b) so I'm sorry for the hard time I'm causing you. I hope you understand what I wrote.

Circular-rectilinear transfer
The metal bar of length l on the figure has an extremity fixed on point P on a circle of the radius a. The other extremity of the bar, point Q, moves in a rectilinear horizontal trajectory.

a) By finding x, the distance between O and Q, determine x in function of angle θ.

b) Supposing that the lengths are expressed in centimeters and that the variation of the angle is 2 radians per seconds in anti-clockwise, find the speed at which the point Q is moving when θ = π/2

c) What do we need to calculate if we want to find for which angle θ point P is moving the fastest.

2. law of cosines ...

$\displaystyle L^2 = a^2 + x^2 - 2ax\cos{\theta}$

$\displaystyle \frac{d}{dt}(L^2 = a^2 + x^2 - 2ax\cos{\theta})$

$\displaystyle 0 = 2x \frac{dx}{dt} + 2ax\sin{\theta}\frac{d\theta}{dt} - 2a\cos{\theta}\frac{dx}{dt}$

when $\displaystyle \theta = \frac{\pi}{2}$ , $\displaystyle x = \sqrt{L^2 - a^2}$

$\displaystyle 0 = 2\sqrt{L^2 - a^2} \frac{dx}{dt} + 4a\sqrt{L^2 - a^2}$

$\displaystyle \frac{dx}{dt} = -2a$ units/sec

for part (c), point P will move at a constant speed if $\displaystyle \frac{d\theta}{dt}$ is constant ... does the problem say that it is variable?

3. Nope not specified at at all. Every part of the problem is there. For part (c) I'll manage to solve it on my own or I,l ask a classmate for specifications... Thank so much for the solution. I didn't actually think it to be that simple... I guess I wasn't thinking about the law of cosines.