Related Rates (some examples)
Lecture notes coming soon...
- Q** A candle is placed a distance l1 from a thin block of wood of height H. The block is a distance l2 from a wall as shown in figure 7.1. The candle burns down so that the height of the flame, h1 decreases at the rate of 3 cm/hr. Find the rate at which the length of the shadow y cast by the block on the wall increases. ( note: your answer will be in terms of the constants l1 and l2).
- A** Note that a decrease in the candle height is equivalent to an increase in H. Thus we can use similar triangle to write H/l1 = y/(l1 + l2). Now differentiate the equation with respect to time t, to get H'/l1 = y'/(l1 + l2). Since H' = 3cm/hr (note that it is positive because it's increasing in length), y' = 3(1 + l2/l1) cm/hr.
- Q** Helium is pumped into a spherical balloon at a rate of 4 cubic feet per second. How fast is the radius increasing after 3 minutes? Note: The volume of a sphere is given by :