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   1. The width of a rectangle is increasing at a rate of 2 cm/sec. and its length is
      increasing at a rate of 3 cm/sec. At what rate is the area of the rectangle increasing
      when its width is 4 cm and its length is 5 cm?




                                                                    Ans. 22 cm 2 sec
   2. Digging in your backyard, you accidentally break a town water line. Water,
      bubbling up at a rate of 1 cubic inch per second, is forming a circular pond of
      depth 0.5 inch in your backyard. How quickly is this pond covering your lawn?
      (i.e. how quickly is the surface area of this pond increasing?)




                                                                      Ans. 2in 2 sec
   3. A police car, approaching a right-angled intersection from the north is chasing a
      speeding car that has turned the corner and is now moving straight east. When the
      police car is 0.6 mi north of the intersection and the car is 0.8 mi to the east, the
      police determine with the radar that the distance between them and the car is
      increasing at 20 mph. If the police car is moving at 60 mph at the instant ofy

      measurement, what is the speed of the car?

                                                                      police car




                                                                                                          x


                                                                                           speeding car




                                                                    Ans. 70 mph
4. A man 6 ft tall is walking away from a spotlight (L) located on the ground. His
   shadow is cast on a wall 40 ft from the spotlight. If the man is walking at a rate of
   4 ft per second away from the spotlight determine the rate of change of the
   shadow (PQ) when he is half way to the wall.                            y




                                                                                           Q




                                                                                  B

                                                                                      6
                                                                                                   x

                                                                          L       A            P



                                                                          12 ft
                                                                   Ans.
                                                                           5 sec


5. Water runs into a conical tank at a the rate of 9 ft 3 / min . The tank stands point
   down and has a height of 10 ft and a base radius of 5 ft. How fast is the water
   level rising when the water is 6 ft. deep?




                                                                          1 ft
                                                                   Ans.
                                                                           min

6. The Pillsbury dough-boy has decided to bake cookies for the Calculus classes. He
   begins with 40 cm 3 of cookie dough. Rolling the dough into a cylindrical shape
   he notices that the rate of change of the radius of the cylinder is decreasing at .5
   cm per minute. At the instant when the radius of the cylinder is 2cm determine
   the rate of change of the height of the cylinder




                                                                   Ans. 5cm min
7. In the triangle shown above, if  increases at a constant rate of 3 radians per
   minute, at what rate is x increasing in units per minute when x equals 3 units?

                                                                                    5
                                                                                                      x

                                                                          

                                                                  Ans. 12 units min

                                      mi
8. An airplane (pt. A) is flying 600       on a horizontal path that will take it directly
                                      hr
   over an observer (pt. O). The airplane maintains a constant altitude of 7 mi (see
   figure). What is the rate of change of the distance between the observer and the           A
   airplane when x = 5 mi.?

                                                                                      z
                                                                                                  7 mi.


                                                                              O
                                                                                          x

                                                                         3000
                                                                  Ans.         mph
                                                                           74

                                      mi
9. An airplane (pt. A) is flying 600     on a horizontal path that will take it directly
                                      hr
   over an observer (pt. O). The airplane maintains a constant altitude of 7 mi (see
   figure). How fast is the angle  changing when x = 5 mi.?                             A


                                                                                  z
                                                                                              7 mi.


                                                                          O
                                                                                      x




                                                                         2100 rad
                                                                  Ans.
                                                                          37 hr

				
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posted:8/22/2012
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