Rates of Change

Question

A ladder AB of length 5 m has one end A leaning against a vertical wall. The other end B rests on the horizontal ground. When A is at a height of 4 m, it slides down the wall at the rate of 2m s^-1.How fast is the other end,B, sliding along the horizontal ground?

 

Ans: 8/3 m s^-1

Answer 1

We use the Pythagorean Theorem for this problem since a ladder on the ground resting against a wall denotes a right triangle.

 

a² + b² = c²

 

Take derivatives with respect to time.

 

2a*da/dt + 2b*db/dt = 2c*dc/dt

 

Since the length of the ladder never changes, we can say dc/dt = 0.

 

2a*da/dt + 2b*db/dt = 0

 

a = 4 m

b = 3 m

 

8*da/dt + 6*db/dt = 0

 

da/dt = -2/ms

 

-16 m²/s + 6 m * db/dt = 0

 

db/dt = 16/6 m/s = 8/3 m/s