Question

3. A ladder is leaning against a wall. The ladder is 5 meters long. The top of the

ladder is 3 meters above the ground. The top of the ladder is sliding down at 8 meters/second.
a) How far is the bottom of the ladder from the wall?
b) How fast is the bottom of the ladder sliding away from the wall?

Answer 1

a. 4m

b. 6m/s

Explanation:

wall height = y = 3m

ladder length = L = 5m

distance from bottom of ladder to the wall = x

a. y² + x² = L² -----------eq.(1)

3³ + x² = 5²

x = 4 m

b. How fast is the bottom of the ladder sliding away from the wall? = dx/dt

using eq.1 ---- y² + x² = L²

2y (dy/dt) + 2x (dx/dt) = 0

y (dy/dt) + 2 (dx/dt) = 0

we know that (dy/dt) = -8 m/s

3 (-8) + 4 (dx/dt) = 0

dx/dt = -24 / -4

dx/dt = 6 m/s

Answer 2

1. The bottom of the ladder is 4 meters away from the wall

2. I'm not sure about this one, someone else answer please :D

Explanation:

We can use the Pythagorean Theorem to find how far away the bottom of the ladder is.

The ladder is creating a triangle, with 5 as it's hypotenuse and 3 as one of the left.

`a^2 + 3^2 = 5^2\\a^2 + 9 = 25\\a^2 = 25-9\\a^2 = 16\\a = 4`

I'm sorry I couldn't answer the second one, but I hope this helped!