Question

3 400 29. 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 40 m apart. If the maxi- mum 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) x(40 – x). (a) A boat proceeds at a constant speed of 5 m/s from a point A on the west bank while maintaining a heading perpen- dicular to the bank. How far down the river on the oppo- site bank will the boat touch shore? Graph the path of the boat. (b) Suppose we would like to pilot the boat to land at the point B on the east bank directly opposite A. If we main- tain a constant speed of 5 m/s and a constant heading, find the angle at which the boat should head. Then graph the actual path the boat follows. Does the path seem realistic?

Answer 1

ANSWERS ca) f(x): 3 X1 40-X) 400 The length of the Hime taken to cooss dx : distance speed dx 5 Horizontal distance travelled dosing dae length towords north = Speed x time se (40-x) et en -> 1) 400 40 da Total distance travelled by boat tourods 5mls North 40 3 400 XC40-2) de 40 [oo [ 1993+ (01_40) x 400 x 40 x 3 400 = 402 10X2X5 - 1600 100 16m. b) Now boat Velocity 1 o 10 Stream is 5COS SO

Boat velocity towards north 3 400 De (40-2) -5 sino B (1) distance travelled to north 40 02 I oO 2040-2) - 5 Bino) 50050 A -0 5COSO 40 40 I 22C40-x) 5sino dx 400 5 sino → 16 = 40 sin sino = 16 40 allo Sin (3) 0 : 23.578 28-60 "hanking you please give like it helps to motivate me to do more wook friend