An airplane ying north at 800 miles per hour passes over a certain town at noon. A second airplane going east at 500 miles per hour is directly over the same town 15 minutes later. if the airplanes are ying at the same altitude. how fast will they be separating at 1:15 F'.M.? miles per hour A woman standing on a cliff is watching a motorboat through a telescope as the boat approaches the shoreline directly below her. If the telescope is 100 feet above the water level and if the boat is approaching at 20 feet per seconds. at what rate is the angle of the telescope changing when the boat is 200 feet from the shore? negative radian per second As the sun sets behind a 100foot building, the building's shadow grows. How fast is the shadow growing (in feet per second) when the sun's ray make an angle of 1r_/ 3 radians? Webster City monitors the height of the water in its cylindrical water tank with an automatic recording device. Water is constantly pumped into the tank at the rate of 2300 cubic feet per hour. If the radius of the tank is 20 feet and the water level fell at the rate of 4 feet per hour at ? AM.' at what rate was water being used exactly at that time? cubic feet per hour Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other (both are growing larger as more gravel is dumped). How fast is the height of the pile increasing when the pile is 11 feet high? Recall that the volume ofa right circular cone with height h and radius ofthe base r is given by feet per minute Aspherical snowball is melting in such a way that its diameter is decreasing at rate of 0.3 cmfmin. Assume that the snowball remains perfectly spherical as it melts. At what rate is the volume of the snowball decreasing when the diameter is 10 cm? Recall that the volume ofa sphere is given by the formula V = 51173. (Note that the answer is a positive number, since you are being asked for a rate of decrease). cm3l'min Find fly if (a) y = 3:3'1 732+ 22,113; 2 dz. (a) y = m. dy 2 dz. (a) y = 3511(33'i 732 + 2:), dy 2 dz. Suppose you need good approximations to v 4.1 and V8.9. but your calculator has died. What might you do? Use differentials and the technique outlined in Example 2 page 144. JEN KN