3) Related Rates- Water in a Tank 4) Complete 'Related Rates (Volume & Surface Area)' pre-quiz Watch Spencer Munroe (APC '14) explain TW question #2 here.
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Answer
6.2 – Related Rates The Calculus Page 2 of 2 #3) A study of urban pollution predicts that sulfur oxide emissions in a city will be 5( T)=0.1 T2+20 T+2 tons, where x is the population (in thousands). The population of the city t years from now is expected to be T=20√ P+800 thousand people. AP Calculus AB (Vahsen) Name: 2.6 Related Rates Problem Set Show all work to receive full credit! The Kite A kite is moving horizontally away from the person flying it with a speed of 7 the kite flyer. M sec at an altitude of 30 m. Determine how fast the string is being let out when the kite is 50 m from.
Work Step by Step
This video lesson explores the concept of Related Rates, which is the study of what is happening over time.
To solve problems with Related Rates, we will need to know how to differentiate implicitly, as most problems will be formulas of one or more variables.
But this time we are going to take the derivative with respect to time, t, so this means we will multiply by a differential for the derivative of every variable!
But don't let this confused you, as there are only four basic steps when problem-solving with Related Rates:
- Write down every given information or quantity, even what you're looking for, and make a sketch.
- Determine the equation needed to solve for your unknown quantity.
- Take the derivative implicitly, not forgetting to multiply by your differential for every single variable!
- Plug in all of your given information or quantities and solve.
And here's a big hint…
…most of the time all we have to do is find an equation that relates the rate we're looking for to a rate that we already know, as Paul's Online Notes so nicely states.
This means we need to look for geometric shapes, known formulas, and ratios.
Ladder Sliding Down a Wall
Together we will solve these 8 classic questions:
- Pebble Dropped In Pond
- Air Being Pumped Into A Balloon
- Edges Of Cube Expanding
- Radar Tracking Station & Airplane Flight Path
- Sand Falling onto a Conical Pile
- Water Pouring into a Conical Tank
- Boat Pulled into a Dock
- Ladder Sliding Down a Wall
How to Solve Related Rates – Video
1 hr 35 min
- Write down every given information or quantity, even what you're looking for, and make a sketch.
- Determine the equation needed to solve for your unknown quantity.
- Take the derivative implicitly, not forgetting to multiply by your differential for every single variable!
- Plug in all of your given information or quantities and solve.
And here's a big hint…
…most of the time all we have to do is find an equation that relates the rate we're looking for to a rate that we already know, as Paul's Online Notes so nicely states.
This means we need to look for geometric shapes, known formulas, and ratios.
Ladder Sliding Down a Wall
Together we will solve these 8 classic questions:
- Pebble Dropped In Pond
- Air Being Pumped Into A Balloon
- Edges Of Cube Expanding
- Radar Tracking Station & Airplane Flight Path
- Sand Falling onto a Conical Pile
- Water Pouring into a Conical Tank
- Boat Pulled into a Dock
- Ladder Sliding Down a Wall
How to Solve Related Rates – Video
1 hr 35 min
- Overview of Related Rates + Tips to Solve Them
- 00:02:58 – Increasing Area of a Circle
- 00:12:30 – Expanding Volume of a Sphere
- 00:21:15 – Expanding Volume of a Cube
- 00:26:32 – Calculate the Speed of an Airplane
- 00:39:13 – Conical Sand Pile
- 00:51:19 – Conical Water Tank
- 00:59:59 – Boat & Winch
- 01:09:13 – Ladder Sliding Down A Wall
Related Rates
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