CALCULUS Higher Concepts of Mathematics Take the  derivative  of both  sides  of this  equation  with respect  to time t.   The c, representing the length of the ladder, is a constant. 2a     da dt 2b db dt a     da dt b db dt But, db/dt is the velocity at which the bottom end of the ladder is moving  away  from  the  wall,  equal  to  2  ft/s,  and  da/dt  is  the downward  velocity  of  the  top  end  of  the  ladder  along  the  wall, which  is  the  quantity  to  be  determined.    Set  b  equal  to  10  feet, substitute the known values into the equation, and solve for a. a²   c²   b² a   c²   b² a   (26  ft)²   (10  ft)² a   676  ft²   100  ft² a   576  ft² a = 24 ft a     da dt b db dt     da dt b a db dt     da dt 10  ft 24  ft (2  ft/s)     da dt 0.833  ft/s Thus,  when  the  bottom  of  the  ladder  is  10  feet  from  the  wall  and  moving  at 2ft/sec., the top  of the ladder  is moving downward at  0.833 ft/s.   (The negative sign indicates the downward direction.) MA-05 Page 40 Rev. 0