Homework SourseA woman wants to go from her house to a cabin as quickly as
A woman wants to go from her house to a cabin as quickly as possible. The cabin is situated 4 km down from the house on the opposite side of a lake with straight shorelines. The lake is 2km wide. She is planning first to run along the shore the distance of d km and then swim straight to the cabin. If she can run at 12km/h and swim at 4km/h, the distance d that minimizes travel time is?
Solution
let total time taken :
d/12 + sqrt [ [23 - d]2 + 4 ] /4 = T
we have to minimize T
take diff wrt to d
: 1/12 + [ -2[23 - d]/ 8*sqrt[[23 - d]2 + 4]] = 0
: 1/3 = [23 - d]/sqrt[[23 - d]2 + 4]
[23 - d]2 + 4 = 9 [23 - d]2
: 1/2 = [23 - d]2
: 1/2 = 23 - d
d = 23 - 1/2 answer !!!!!
d = 23 + 1/2 is not possible as it is greater than 23
