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Related Rates Project

Related Rates Project. May 28-29 Related Rates Review May 30 Groups Due May 30 Related Rates Packet Due June 4 Related Rates Project Topic Due June 9 Related Rates Presentations Begin. Related Rates Project.

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Related Rates Project

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  1. Related Rates Project May 28-29 Related Rates Review May 30 Groups Due May 30 Related Rates Packet Due June 4 Related Rates Project Topic Due June 9 Related Rates Presentations Begin

  2. Related Rates Project • You will be reenacting a related rates problem of your choice (see packet for ideas) • You may create your own problem • Use your own measured rates and values • June 9-13 each group will present their related rates problem • Presentations will either be reenactments in class or a video of the reenactment done out of class • A write-up of the problem is due June 9 • Groups of maximum 3-4

  3. Related Rates Review • When we use implicit differentiation, we obtain dy/dx, or the change of y in terms of x. • In many real life situations, each quantity in an equation changes with time (or another variable) • In this case, any derivative we find is called a related rate, since each rate in the derivative is related to each other

  4. Related Rates Steps • 1) Make a simple sketch, if possible • 2) Identify what rate you are looking for • 3) Set up an equation relating ALL of the relevant quantities • 4) Differentiate both sides of the equation in terms of the variable you want • if you want dv/dt, you differentiate in terms of t • 5) Substitute in values we know • 6) Solve for the remaining rate

  5. Ex 1 • A 5-meter ladder leans against a wall. The bottom of the ladder is 1.5 m from the wall at time t=0 and slides away from the wall at a rate of 0.8m/s. Find the velocity of the top of the ladder at time t=1

  6. Ex 2 • Water pours into a fish tank at a rate of 0.3 m^3 / min. How fast is the water level rising if the base of the tank is a rectangle of dimensions 2 x 3 meters?

  7. Ex 3 • Water pours into a conical tank of height 10 m and radius 4 m at a rate of 6 m^3/min • A) At what rate is the water level rising when the level is 5 m high? • B) As time passes what happens to the rate at which the water level rises?

  8. Ex 4 • A spy uses a telescope to track a rocket launched vertically from a launching pad 6km away. At a certain moment, the angle between the telescope and ground is equal to pi/3 and is changing at a rate of 0.9 radians/min. What is the rocket’s velocity at that moment?

  9. Related Rates Project • May 30 Groups Due • June 2 Related Rates Packet Due • June 4 Related Rates Project Topic Due • June 9 Related Rates Presentations Begin Today • June 9 Write-up Due (Regardless of when you present)

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