Related Rates
Authored by Jacob Taylor
Physics
12th Grade
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
1. A ladder is 10 meters long and is leaning against a wall. If the bottom of the ladder is sliding away from the wall at a rate of 2 m/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 meters from the wall?
1 m/s
-5/3 m/s
0 m/s
2 m/s
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
2. A spherical balloon is being inflated at a rate of 10 cubic centimeters per second. How fast is the radius of the balloon increasing when the radius is 5 cm?
The radius of the balloon is increasing at a rate of 1/4π cm/s when the radius is 5 cm.
The radius of the balloon is increasing at a rate of 2/π cm/s when the radius is 5 cm.
The radius of the balloon is increasing at a rate of 10π cm/s when the radius is 5 cm.
The radius of the balloon is increasing at a rate of 5 cm/s when the radius is 5 cm.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
3. A conical tank is being filled with water at a rate of 3 cubic meters per minute. If the radius of the tank is 4 meters and the height is 6 meters, how fast is the water level rising when the water is 5 meters deep?
The water level is rising at a rate of 2.5 meters per minute when the water is 5 meters deep.
The water level is rising at a rate of 0.6 meters per minute when the water is 5 meters deep.
The water level is rising at a rate of 1.5 meters per minute when the water is 5 meters deep.
The water level is rising at a rate of 4 meters per minute when the water is 5 meters deep.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
4. A kite is flying at a height of 100 meters. If the string is being reeled in at a rate of 5 m/s, how fast is the angle between the string and the ground changing when there is 200 meters of string out?
The rate at which the angle between the string and the ground is changing when there is 200 meters of string out is 10 m/s.
The rate at which the angle between the string and the ground is changing when there is 200 meters of string out is 3 m/s.
The rate at which the angle between the string and the ground is changing when there is 200 meters of string out is 4 m/s.
The rate at which the angle between the string and the ground is changing when there is 200 meters of string out is 2.5 m/s.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
5. A cylindrical tank is being filled with water at a rate of 2 cubic meters per minute. If the radius of the tank is 3 meters and the height is 10 meters, how fast is the water level rising when the water is 5 meters deep?
The water level is rising at a rate of 3/9π meters per minute.
The water level is rising at a rate of 1/9π meters per minute.
The water level is rising at a rate of 2/9π meters per minute.
The water level is rising at a rate of 5/9π meters per minute.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
6. 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?
1/5 m/s
2 m/s
-1/5 m/s
0 m/s
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
7. A 15-foot ladder is leaning against a wall. If the bottom of the ladder is sliding away from the wall at a rate of 2 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 9 feet from the wall?
5 ft/s
10 ft/s
15 ft/s
3 ft/s
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