Math
posted by Anonymous .
A 15 ft ladder leans against a wall. The bottom of the ladder is 3 ft from the wall at time t=0 and slides away from the wall at a rate of 3ft/sec.
Find the velocity of the top of the ladder at time t=3.

Let the foot of the ladder be x feet from the wall
let the height of the ladder be y feet
then x^2 + y^2 = 225
differentiate with respect to t, this is a "related rate problem"
2x dx/dt + 2y dy/dt = 0 (1)
when t=3 sec,
x = 9 feet (you knew the rate)
then 81+y^2=225
y=12 feet
sub x=9, y=12, dx/dt = 3 into (1) and solve for dy/dt
I got dy/dt = 9/4 ft/sec
(the negative value shows that y was decreasing at 9/4 ft/sec at that instant) 
a building is 3ft. from a 8ft. fence that surround propert a worker wants to wash a window in the building 13ft. from the ground. he will need what size ft. ladder
Respond to this Question
Similar Questions

Calculus
A 15 ft ladder leans against a wall. The bottom of the ladder is 4 ft from the wall at time t=0 and slides away from the wall at a rate of 3ft/sec. Find the velocity of the top of the ladder at time t=2. The velocity of ladder at time … 
Calculus
A 18 ft ladder leans against a wall. The bottom of the ladder is 4 ft from the wall at time t=0 and slides away from the wall at a rate of 3ft/sec. Find the velocity of the top of the ladder at time t=1. The velocity of ladder at time … 
Calculus
1a. 15 ft ladder is placed against a vertical wall. the bottom of the ladder is sliding away from the wall at a rate of 2 ft/sec. How fast is the top of the ladder sliding down the wall when the bottom of the ladder is 9 ft from the … 
calculus 1
a ladder 20 ft. long rests against a vertical wall.If the bottom of a ladder slides away from the wall at a rate of 4 ft./sec, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 12 ft. from the … 
calculus
a ladder 6 feet long leans against a vertical building. the bottom of the ladder slides away from the building horizontally at rate of 1/2 ft/sec. A) at what rate is the top of the ladder sliding down the wall when the bottom of the … 
Calculas
A 13ft ladder is placed against a verticle wall. Suppose the bottom of the ladder slides away from the wall at a constant rate of 2 feet per second. How fast is the top of the ladder sliding down the wall (negitive rate) when the bottom … 
AP calc bc
A 25ft ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.18 ft/sec, how fast, in ft/sec, is the top of the ladder sliding down the wall, at the instant when the bottom of the … 
calculus
A 25ft ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.18 ft/sec, how fast, in ft/sec, is the top of the ladder sliding down the wall, at the instant when the bottom of the … 
caculus
A 10ft ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/sec, how fast, in ft/sec, is the top of the ladder sliding down the wall, at the instant when the bottom of the ladder … 
calculus
A 15ft ladder rests against a vertical wall. If the top of the ladder slides down the wall at a rate of 0.33 ft/sec, how fast, in ft/sec, is the bottom of the ladder sliding away from the wall, at the instant when the bottom of the …