4.6 Rates and Related Rates.notebook
November 21, 2014
Section 4.6: Rates and Related Rates
Example:
1. A spherical snowball is melting. Its radius decreases at a constant rate of 2 cm per minute from an initial value of 70 cm. How fast is the volume decreasing half an hour later?
4.6 Rates and Related Rates.notebook
November 21, 2014
2. A skydiver of mass m jumps from a plane at time t = 0. Under certain asumptions, the distance, s(t), he has fallen in time t is given by
s(t) = m2g
k2
( mkt + e
­kt/m
(
­ 1
for some positive constant k.
(a) Find s'(0) and s''(0) and interpret in terms of the skydiver.
(b) Relate the units of s'(t) and s''(t) to the units of t and s(t)
4.6 Rates and Related Rates.notebook
November 21, 2014
3. A spherical snowball melts in such a way that the instant at which its radius is 20 cm, its radius is decreasing at 3 cm/min. At what rate is the volume of the ball of snow changing at that instant?
4.6 Rates and Related Rates.notebook
Assignment 4.6: (part 1)
Page 210 #'s 1 ­ 9 odd
November 21, 2014
4.6 Rates and Related Rates.notebook
November 21, 2014
Section 4.6: Rates and Related Rates
Example:
4. The graph below (also on page 208) shows the fuel consumption, g, in miles per gallon, of a car traveling at v mph. At one moment, the car was going 70 mph and its deceleration was 8000 miles/hour2. How fast was the fuel consumption changin at that moment? Include units.
4.6 Rates and Related Rates.notebook
November 21, 2014
4.6 Rates and Related Rates.notebook
November 21, 2014
5. (a) A 3­meter ladder stands against a high wall. The foot of the ladder moves outward at a speed of 0.1 meter/sec when the foot is 1 meter from the wall. At that moment, how fast is the top of the ladder falling? What if the foot had been 2 meters from the wall? 4.6 Rates and Related Rates.notebook
November 21, 2014
5. (b) If the foot of the ladder moves out at a constant speed, how does the speed at which the top falls change as the foot gets farther out?
4.6 Rates and Related Rates.notebook
November 21, 2014
6. An airplane, flying at 450 km/hr at a constant altitude of 5 km, is approaching a camera mounted on the ground. Let θ be the angle of elevation above the ground at which the camera is pointed. When θ = π/3, how fast does the camera have to rotate in order to keep the plane in view?
4.6 Rates and Related Rates.notebook
November 21, 2014
Assignment 4.6: (part 2)
Page 211­212 #'s 15 ­ 21 odd, 27