PROBLEM I A heavy stone of8 kg is dropped into a lake, hitting the water with a speed of 7 m/s. Assuming we have a drag force ofthe form FD = 1317 with b = 120 kg/s, how long does it for the stone to reach 10% of its original speed? Please use 9 = 9.8 m/sz. PROBLEM 2 A boat traveling at 4 m/s runs out of fuel, causing the engine to turn off. Because of the drag force FD = 1312 with the water, the boat immediately starts to slow down. In this problem we do not know the value of b, but we do know that the speed of the boat has been reduced to 2 m/s exactly 5 seconds after the engine stopped. How far does the boat travel before it comes to a complete stop? Solution Problem 1 Page1 m = okg vi = Tom/s of = 10% of Fm/s = 0.7m/s to = by ( where b = 120 kg / sec ) my - Fp = mall of = m dy mg - by OR at = - may ( by- mg on integrating 0. 7 at = - m by- mg 7 m b [ log ( by-ma ) 70" 7 dog ( Q4 - 70 .4) - 109 ( 040 - 70 .4 ) / 120 t = - 0 (0 75 - 2.80 ) 120 t = (- 2.137 120 t = 0. 142 sec So after 0.142 sec Stome Reach 10% of its original speed