A boat on the ocean is 4 mi from the nearest point on a straight shoreline; that point is 14 mi from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant.
Minimize the time traveled, where would she land on shore?
walks at 3 mi/hr and rows at 2 mi/hr
- davidLv 78 months ago
d = dist. rowed
x = dist down the beach where she comes ashore
...x^2 + 4^2 = d^2
distt walked = 14 - x
time rowed = d/r = d / 2
time walked = (14-x)/3
T = d/2 + (14-x)/3
T = sqrt(x^2 + 16)/2 + (14-x)/3
T' = (1/2)(x^2 + 16)^(-1/2) *2x + -1/3
T' = -x/sqrt(x^2 + 16) - 1/3 = 0
x/sqrt(x^2 + 16) = -1/3
sqrt(x^2 + 16) = -3x
x^2 + 16 = 9x^2
8x^2 = 16
x = sqrt 2 ..... (neg will not be a min)
from the point closest to the boat, she should come ashore sqrt 2 miles down the beach from there.
- 冷眼旁觀Lv 78 months ago
This is an incomplete question. To solve it, the speed of rowing boat and that of walking along the shore should be given.