A ball is dropped from a boat so that it strikes the surface of a lake with a speed of 16.5ft/s. While in the water the ball experiences an acceleration of a = 10 - 0.8v, where a and v are expressed in ft/s^2 and ft/s, respectively. Knowing the ball takes 3 s to reach the borrom of the lake, determine (a) the depth of the lake, (b) the speed of the ball when it hits the bottom of the lake.