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ABC DC 4.5.6 On Related Rates

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Last updated about 5 years ago
3 questions
Note from the author:
related rates
This daily check has two questions. Type your final answer in each question, and then upload your work for both problems in #3. Make sure your work includes a diagram, use proper notatipon, and correct units. You have 30 minutes to complete.
6
Question 1
1.

Santa’s reindeer got tired and were not able to fly to the top of the roof. So instead Santa had to climb a 40 foot ladder to get to the chimney on a 25 foot house. Unfortunately, Santa had been eating a bunch of cookies and the base of the ladder started sliding away from the house at a rate of one foot per second. He slid down until he could climb in a second floor window which was 20 feet above ground. What is the rate of change of the angle of Santa’s ladder and the ground at that instant in radians?

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Question 2
2.

The Grinch has designed a vacuum that will suck up all the toys in Whoville after Santa delivers them in his new non-aerodynamic sleigh after climbing in the second floor windows. His vacuum, shaped like a right cone with a base of 1000 meters and height of 5000 meters. If the vacuum sucks up toys at the rate of 10,000 cubic meters/second (it’s a good vacuum), what is the change in radius over time when the vacuum is half filled (half of height)?

Question 3
3.

Upload a copy of your work for both problems. You must show your work to receive credit for this daily check.