# Help solve this related rate problem

• Jun 18th 2009, 12:23 AM
zEr0ne
Help solve this related rate problem
A conical pendulum consists of a mass m, attached to a string of fixed length L, that travels around a circle of radius r at a fixed velocity v. As the velocity of the mass is increased, both the radius and angle x increase. Given that v^2 = r*g*tan(x), where g is a gravitational constant, find the relationship between the related rates

a) dv/dt and dx/dt
b) dv/dt and dr/dt
• Jun 18th 2009, 04:31 AM
skeeter
Quote:

Originally Posted by zEr0ne
A conical pendulum consists of a mass m, attached to a string of fixed length L, that travels around a circle of radius r at a fixed velocity v. As the velocity of the mass is increased, both the radius and angle x increase. Given that v^2 = r*g*tan(x), where g is a gravitational constant, find the relationship between the related rates

a) dv/dt and dx/dt
b) dv/dt and dr/dt

$\displaystyle \frac{d}{dt}[v^2 = rg\tan{x}]$

$\displaystyle 2v \cdot \frac{dv}{dt} = g\left[r \cdot \sec^2{x} \cdot \frac{dx}{dt} + \tan{x} \cdot \frac{dr}{dt}\right]$

note that $\displaystyle r = L\sin{x}$

so ...

$\displaystyle \frac{dr}{dt} = L\cos{x} \cdot \frac{dx}{dt}$

and

$\displaystyle \frac{dx}{dt} = \frac{\sec{x}}{L} \cdot \frac{dr}{dt}$

given the above relationships, you should be able to finish up and answer the questions.