1. SPECIALIST MATHS Calculus Week 4 Related Rates

2. Related rate give relationship between two or more variables whose value are changing with time. An example could be the relationship in the rate of change in the radius of a balloon to the rate of change in its volume as it is being blown up.

3. RELATED RATES Problem Solving Techniques Draw a large clear labeled diagram Write down information Distinguish between variables and constants Write an equation connecting the variables Differentiate the equation with respect to time Solve for the given case

4. Ideas for writing an equation between variables and constants Pythagoras's theorem Similar triangles Right angled triangle trigonometry Sine and Cosine rules

5. Example 7 Car P leaves town A at 1:30pm moving north at 60 km/hr. At 2:30pm car Q leaves town A moving east at 80 km/hr. At what rate is the distance between cars P and Q changing at 3:30pm.?

6. Solution to example 7 A P Q

7. Continued

8. Example 8 The surface area of a balloon is increasing at a rate of 8cm 2 /sec Find the rate that the air is being pumped into the balloon, ( ie the rate the volume of air in the balloon is increasing) the instant when the radius is 10 cm.

9. Solution to Example 8

10. Continued

11. Example 9 (using trig) An observer watches a rocket being launched at a distance of 1000 km from the launch pad. At the instant when the angle of elevation of the rocket is 45 o the angle is changing at a rate of 1 radian per second. Determine the vertical velocity of the rocket at this instant.

12. Solution to Example 9

13. Continued

14. This Week Text pages 226 to 232, and 247 t0 250. Exercise 6F Q 1 – 12 Exercise 7C Q 1 - 9