Homework Help: Calculus 1

Posted by Tina P on Tuesday, December 7, 2010 at 10:20am.

A ladder 10ft long rests against a vertical wall. If the bottom on the ladder slides away from the wall at 2 ft/s, how fast is the angle ladder makes with the ground changing when the bottom of the ladder is 5 ft from the wall.

Calculus 1 - Reiny, Tuesday, December 7, 2010 at 10:28am
Let the foot be x ft from the wall, let the angle formed by the ladder at the ground be Ų

given: dx/dt = 2 ft/s
find: dŲ/dt when x = 5

x/10 = cosŲ
x = 10cosŲ
dx/dt = -10sinŲ dŲ/dt

when x=5,
height^2 + 5^2 = 10^2
height = √75

2 = -10(√75/10) dŲ/dt
dŲ/dt = - 2/√75 radians/second
= appr. - .23 rad/s

Answer this Question

Related Questions

Calculus - A ladder 10 ft long rests against a vertical wall. If the bottom on ...
Calculus Ladder Problem - A ladder 20 ft long rests against a vertical wall. Let...
calculus - A ladder 10 ft long rests against a vertical wall. let θ be ...
calculus - A ladder 14 ft long rests against a vertical wall. Let \theta be the ...
Math - a ladder 10 ft long rests against a&...
math - A ladder 10 ft long rests against a vertical wall. let θ be the ...
math - A ladder 14 ft long rests against a vertical wall. Let \theta be the ...
Math - A ladder 20 ft long rests against a vertical wall. Let \theta be the ...
Math - A ladder 20 ft long rests against a vertical wall. Let \theta be the ...
Math - A ladder 10 ft long rests against a vertical wall. If the bottom of the ...

For Further Reading

First Name:
School Subject:
Answer: