AP Calculus Name ___________________________________ Period ___
Section 3.9c
AP Calculus Name ___________________________________ Period ___
Section 3.9c
1.
A street light is mounted at the top of a 15 foot pole. A man 6 feet tall walks
away from the pole with a speed of 5 feet per second along a straight path. How
fast is the tip of the shadow moving when he is 40 feet from the pole?
1. A street light is mounted at the top of a 15 foot pole. A man 6 feet tall walks
away from the pole with a speed of 5 feet per second along a straight path. How
fast is the tip of the shadow moving when he is 40 feet from the pole?
2.
A boat is pulled into a dock by a rope attached to the bow of the boat and passing
through a pulley on the dock that is 1 meter higher than the bow of the boat. If
the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock
when it is 8 meters from the dock?.
2. A boat is pulled into a dock by a rope attached to the bow of the boat and passing
through a pulley on the dock that is 1 meter higher than the bow of the boat. If
the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock
when it is 8 meters from the dock?.
3.
A spot light on the ground shines on a wall 12 meters away. If a man 2 meters
tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast
is his shadow on the building decreasing when he is 4 meters from the building?
3. A spot light on the ground shines on a wall 12 meters away. If a man 2 meters
tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast
is his shadow on the building decreasing when he is 4 meters from the building?
4.
A man starts walking north at 4 ft/s from a point P. Five minutes later a woman
starts walking south at 5 ft/s from a point 500 feet due east of P. At what rate are
the people moving apart 15 minutes after the woman starts walking?
4. A man starts walking north at 4 ft/s from a point P. Five minutes later a woman
starts walking south at 5 ft/s from a point 500 feet due east of P. At what rate are
the people moving apart 15 minutes after the woman starts walking?
5.
A man is standing on a pier and pulling a boat inward by pulling a rope at the
rate of 2 meters per second. The end of the rope is 3 meters above the water
level. How fast is the boat approaching the base of the pier when 5 meters of
rope are left to pull in? Disregard sagging of the rope and assume the rope is
attached to the boat at water level.
5 A man is standing on a pier and pulling a boat inward by pulling a rope at the
rate of 2 meters per second. The end of the rope is 3 meters above the water
level. How fast is the boat approaching the base of the pier when 5 meters of
rope are left to pull in? Disregard sagging of the rope and assume the rope is
attached to the boat at water level.
6.
A woman 1.6 meters tall is walking away from a lamp post 10 meters tall. If the
woman is walking a speed of 1.2 m/s, how fast is her shadow increasing when
she is 15 m from the lamp post?
6. A woman 1.6 meters tall is walking away from a lamp post 10 meters tall. If the
woman is walking a speed of 1.2 m/s, how fast is her shadow increasing when
she is 15 m from the lamp post?
7.
A boat is being pulled to shore by a rope attached to a windlass atop of a pier.
The height of the wind lass above the water is 6 m, and the rope is being would
in at the rate of 5 m/min. How fast is the boat approaching the shore when it is
8 m away.
7. A boat is being pulled to shore by a rope attached to a windlass atop of a pier.
The height of the wind lass above the water is 6 m, and the rope is being would
in at the rate of 5 m/min. How fast is the boat approaching the shore when it is
8 m away.
Check:
−
8
35
65
8
Check:
−
5
2
25
3
≈ 8.98
−
−
25
4
3
5
−
8
35
65
8
−
5
2
25
3
≈ 8.98
−
−
25
4
3
5