# Math Help - Curvlinear motion- ladder problem

1. ## Curvlinear motion- ladder problem

A ladder is resting against a vertical wall.The top slides down in the -y direction and the bottom in the -x direction.
What is dtheta/dt (where theta is the angle btw x axis and ladder)when the top of the ladder has -2.6m/s j and the angle btw the x axis and ladder is 26deg.

I have worked out that the i component of vel is 0.634039m/s,but dont know how to calculate dtheta/dt.
Length of ladder is 0.155meters

2. This is a related rates problem. You need a general relationship between theta and y. After you get that, you can differentiate it (possibly using implicit differentiation) to get a relationship between dtheta/dt and dy/dt.

3. Originally Posted by heatly
A ladder is resting against a vertical wall.The top slides down in the -y direction and the bottom in the -x direction.
What is dtheta/dt (where theta is the angle btw x axis and ladder)when the top of the ladder has -2.6m/s j and the angle btw the x axis and ladder is 26deg.

I have worked out that the i component of vel is 0.634039m/s,but dont know how to calculate dtheta/dt.
Length of ladder is 0.155meters
a ladder $L = 0.155 \, m$ ... for a flea circus?

$\theta = \arctan\left(\frac{y}{x}\right)$

$\displaystyle \frac{d\theta}{dt} = \frac{x \cdot \frac{dy}{dt} - y \cdot \frac{dx}{dt}}{x^2} \cdot \frac{x^2}{x^2+y^2} = \frac{x \cdot \frac{dy}{dt} - y \cdot \frac{dx}{dt}}{L^2}$