Question

A ladder 20 feet long leans against a wall and the foot of the
ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile,
a firefighter is climbing up the ladder at a rate of 2 feet/sec.
When the firefighter has climbed up 6 feet of the ladder, the
ladder makes an angle of *π*/3 with the ground. Answer the
two related rates questions below. (Hint: Use two carefully labeled
similar right triangles.)

(a) If *h* is the height of the firefighter above the
ground, at the instant the angle of the ladder with the ground is
*π*/3, find *dh/dt=*

feet/sec.

(b) If *w* is the horizontal distance from the firefighter
to the wall, at the instant the angle of the ladder with the ground
is *π*/3, find *dw/dt*=

feet/sec.

Answer #1

17-foot ladder leans against a wall. The base of the ladder is
11 feet away from the wall. You push the ladder towards the wall at
a rate of 1.5 ft/s. How fast is the angle between the ladder and
the floorchanging after 2 seconds?

You lean your 5 foot long ladder up against the wall. However, a
cat decides to rub up against the bottom of the ladder, causing it
to slide down the wall. If the bottom of the ladder is sliding
across the floor at a rate of 1 foot per minute, how fast is the
ladder sliding down the wall when it is 3 feet from the ground?

The top of a 5-foot ladder is sliding down a wall at a rate of 7
feet per second. How fast is the base of the ladder sliding away
from the wall at the instant when the top of the ladder is 3 feet
from the ground?

a ladder 15 m long leans against a wall. The ladder slides down
the wall at a rate of 1.5m/s. What is the rate of change of the
angle at the ground when the ladder is 6m from the wall.

A ladder 25 feet long is leaning against the wall of a house.
The base of the ladder is pulled away from the wall at a rate of 2
feet per second.
(a) What is the velocity of the top of the ladder when the base
is given below?
7 feet away from the wall
ft/sec
15 feet away from the wall
ft/sec
20 feet away from the wall
ft/sec
(b) Consider the triangle formed by the side of the...

A 2525-foot ladder is placed against a vertical 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 when the bottom is 20 feet from the
wall?
The ladder is sliding down the wall at a rate of __ ft/sec

The top of a 50-foot ladder is sliding down a wall at a rate of
15 feet per second. How fast is the base of the ladder sliding away
from the wall at the instant when the top of the ladder is 30 feet
from the ground? HINT [See Example 2.]

A 18 ft ladder leans against a wall. The bottom of the ladder
slides away from the wall at a rate of 3ft/sec
How fast is ladder sliding down the wall when the base of the
ladder is 10 ft away from the wall?
ft/sec.
Round your answer to three decimal places.

A) A ladder 25 feet long is leaning against a wall. If the foot
of the ladder is pulled away from the wall at the rate of 2 feet
per second, how fast will the top of the ladder be dropping when
the base is 7 feet from the wall?
B) A radar antenna, making one revolution every 3 seconds (one
revoluton is 2π radian), is located on a ship that is 5 km from a
straight shoreline. How fast...

A 26 foot ladder is
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base of the ladder is sliding away from the wall.
At what rate is the ladder sliding away from the wall when the
base of the ladder is 10 feet from the wall?
Would you expect the same rate when
the ladder is any distance from the wall?
Would you expect
your answer to be positive when the base is any...

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