# Math Help - Rate of change - speed problem.

1. ## Rate of change - speed problem.

A ladder 5.1m long is placed on a level ground against a vertical wall. The foot of the ladder is pushed towards the wall at 1.5m/s. At what rate is the top of the ladder rising when its bottom is 2.4m from the wall?

2. Originally Posted by bubbles73
A ladder 5.1m long is placed on a level ground against a vertical wall. The foot of the ladder is pushed towards the wall at 1.5m/s. At what rate is the top of the ladder rising when its bottom is 2.4m from the wall?
We have a right angled triangle, with sides x,y, and r.

r is the hypotenuse, with a length of 5.1
x is given as 2.4

We solve for y and find it is 4.5

$x^2 + y^2 = r^2$

Differentiate.

$2x \frac{dx}{dt} + 2y \frac{dy}{dt} = 0$ (Because r is a constant.)

$2(2.4)(1.5) + 2(4.5) \left( \frac{dy}{dt} \right) = 0$

Solve for $\frac{dy}{dt}$