Download ap calculus lesson 22 related rates day 32

AP Calculus AB Lesson 22 on Related Rates Problems Day 3
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Related Rates Problems Where The Angle Is Changing:
Example 1:
A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder
slides away from the wall at a rate of 1 ft/s, how fast is the top of the
ladder sliding down the wall when the bottom of the ladder is 6 ft from the
wall?
Recall Answer from Example 2 of first day of related rates was -0.75 ft/sec.
New question: How fast is the angle with the horizontal changing
when the bottom of the ladder is 6 ft from the wall?
Example 2:
An airplane, flying at 450 km/hr at a constant altitude of 5 km, is
approaching a camera mounted on the ground. Let  be the angle of
elevation above the ground at which the camera is pointed. When  =

, how fast does the camera have to rotate in order to keep the plane in
3
view?
AP Calculus AB Lesson 22 on Related Rates Problems Day 3
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Example 3:
A kite 100ft above the ground moves horizontally at speed of 8ft/sec. At
what rate is the angle between the string and the horizontal decreasing
when 200 ft of string has been let out?
Example 4:
A lighthouse is located on a small island 3 km away from the nearest point
P on a straight shoreline and its light makes the four revolutions per
minute. How fast is the beam of light moving along the shoreline when it
is 1 km from P?
Homework p. 212 ( 24, 27)