Example 6:
A street light is mounted at the top of a 15 foot pole. A man 6 ft tall walks away from the
pole with a speed of 5 ft/sec along a straight path. When he is 40 feet from the pole, a) how
fast is the tip of his shadow moving? b) how fast is the length of his shadow changing?
Angle Related Rates
Example 7:
A woman on the ground is watching a jet through a telescope as it approaches at a speed of
10 miles per minute at an altitude of 7 miles. At what rate (in radians per minute) is the
angle of the telescope changing when the horizontal distance of the jet from the woman is
24 miles? When the jet is directly above the woman?
Example 8:
A balloon leaves the ground 500 feet away from an observer and rises vertically at the rate
of 40 feet per minute. At what rate is the angle of inclination of the observer’s line of sight
increasing at the instant the balloon is exactly 500 feet above the ground?
Example 9:
A ladder 13 feet long is leaning against the side of a building. If the foot of the ladder is
pulled away from the building at the rate of 0.1 feet per second, how fast is the angle
formed by the ladder and the ground changing at the instant when the top of the ladder is
12 feet above the ground?
Example 10:
A lighthouse is 4 miles from point P along a straight shoreline and the light from his
lighthouse makes 4 revolutions per minute. How fast, in miles per minute is the beam of
light moving along the shoreline when it is 3 miles from point P?