Calculus
posted by Lost student .
a 16 foot ladder is leaning against a building. the bottom of the ladder os sliding along the pavement at 3 ft/s How fast is the top of the ladder moving down when the foot of the ladder is 2 ft from the wall

Let the distance of the bottom of the ladder from the wall be x, and let the distance of the top of the ladder from the floor be y.
x^2 + y^2 = 256
You want to know dy/dt when dx/dt = 3 and x = 2. At that time, y^2 = 252 and y = 15.87
2x *dx/dt + 2y*dy/dt = 0
dy/dt = (x/y)*dx/dt = 0.126 dx/dt
Use that equation to calculate dy/dt
Respond to this Question
Similar Questions

Calculus
related rates: a ladder, 12 feet long, is leaning against a wall. if the foot of the ladder slides away from the wall along level ground,what is the rate of change of the top of the ladder with respect to the distance of the foot of … 
Calculus II
A 24 foot ladder is leaning against a building. Let x be the distance between the bottom of the ladder abd the building and let theta be the angle between the ladder and the ground. Suppose the bottom of the ladder is sliding away … 
Calculus
a 5m ladder rests against a vertical wall. The top of the ladder begins sliding down the wall at 2m/sec, while the foot of the ladder moves away from the base of the wall. How fast is the foot of the ladder moving away from the wall … 
Calculus
The top of a 24 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 4 feet per second. How fast is the bottom of the ladder sliding along the ground when the bottom of the ladder is 7 feet away from … 
Calculus
A 17 foot ladder is leaning against a wall. The bottom of the ladder is moving out away from the wall at 0.6 feet per second. The top of the ladder then begins sliding down the wall. How fast is the top of the ladder going when the … 
Analytical Geometry
A 10 foot long ladder is leaning against a vertical wall with the top of the ladder 8ft from the ground. What is the slope of the ladder? 
Calculus
a 12 foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 1 feet/second, how fast is the top of the ladder moving down when the foor of the ladder is … 
Calculus
a 14 foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 3 feet/second, how fast is the top of the ladder moving down when the foor of the ladder is … 
math
A ladder rests against a vertical pole. The foot of the ladder is sliding away from the pole along horizontal ground. Find the inclination of the ladder to the horizontal at the instant when the top of the ladder is moving 3 times … 
math
A ladder rests against a vertical pole. The foot of the ladder is sliding away from the pole along horizontal ground. Find the inclination of the ladder to the horizontal at the instant when the top of the ladder is moving 3 times …