1. Aim: How do we solve related rate problems?

2. 3. 5 steps for solving related rate problems Diagram Rate Equation Derivative Substitution

3. Types of related rate problems 1. Use Pythagorean Theorem 2. Use basic area formula such as triangle, circle, trapezoid or circumference 3. Use similar triangle 4. Use the formulas of volume such as cylinder, cone, sphere and some complicated shape

4. A 41 ft. ladder is leaning against a wall and the top of it is sliding down the wall while the bottom of it slides away from the wall at 4 ft/sec. How fast is the top sliding when it’s 9 feet above the ground? ladder x y 9 ft

5. A rocket, rising vertically, is tracked by a radar station that is on the ground 5 miles from the launchpad. How fast is the rocket rising when it is 4 miles high and its distance from radar station is increasing at a rate of 2000 miles/hour? station  5 y z

6. Two cars leave an intersection at the same time, one headed east and the other north. The eastbound car is moving at 30 mph while the northbound car is moving at 60 mph. twenty minutes later, what is the rate of change in the perimeter of the right triangle created using the 2 cars and the intersection. x y

8. A boat is being pulled to a dock at the rate of 2 ft/sec. The pulley is 8 feet from the water and the rope is tied to the boat at 1 feet above the water. How fast is the boat approaching the dock when it is 20 feet away? 1 87 x z

9. At noon ship A is 100 km west of ship B. Ship A is sailing south at 35km/hr and ship B sailing north at 25km/hr. How fast is the distance between the ships changing at 4 pm? A B 100 km b a Let distance = c 100 km

11. b = 10

12. A 6-foot-tall man walks away from a 20-foot-street light at a rate of 5 ft/sec. At what rate is the tip of his shadow moving when he is 24 feet from the lightpost and at what rate is the length of his shadow increasing? 20 6 x y light z = x + y Part B Part A

13. Two trucks leave a depot at the same time, Truck A travels east at 40 mph and truck B travels north at 30 mph. How fast is the distance between the trucks changing 6 minutes later when A is 4 miles from the depot and B is 3 miles from the depot? A B C