Water traveling along a straight portion of a river normally flows fastest in the middle, and the speed slows to almost zero at the banks. consider a long straight stretch of river flowing north, with parallel banks 100 m apart. if the maximum water speed is 3 m/s, we can use a quadratic function as a basic model for the rate of water flow x units from the west bank: f(x)= 3/2500x (100-x).

a) a boat proceeds at a constant speed of 5 m/s from point a on the west bank while maintaining a heading perpendicular to the bank. how far down the river on the opposite bank will the boat touch shore? m

b) suppose we would like to pilot the boat to land at the point b on the east bank directly opposite a. if we maintain a constant speed of 5 m/s and a constant heading, find the angle at which the boat should head. ( round to one decimal place.) degreees south of east