Write a function for the time it takes a person to go from the raft to the hut in terms of d?
Write a function for the time it takes a person to go from the raft to the hut in terms of d. {dist= vel x tim
A raft is located 300 meters from a point A on shore. At a point B, on shore, there is a small hut. The distance from pt. A to pt. B is 800 meters. A person can swim at a rate of 2m/s and can jog at a rate of 6m/s. Write a function for the time it takes a person to go from the raft to the hut in terms of d. {dist= vel x time therefore time = dist/vel}
http://s76.photobucket.com/albums/j4/pxgamer/?action=view¤t=8problem.png
plz show steps and thanks in advance
The person swims a distance of √(300² + d²) at 2 m/s for time taken = √(300² + d²)/2
The person runs 800 – d at 6 m/s for time taken = (800 – d)/6
So the total time t(d) = √(300² + d²)/2 + (800 – d)/6
We can go further, and find the d that minimises t(d)
t’(d) = d/(2 √(300² + d²))- 1/6
We set this equal to zero to find the d that minimises t(d)
d/(2 √(300² + d²)) = 1/6
3d/√(300² + d²) = 1
9d²/(90000 + d²) = 1
9d² = 90000 + d²
8d² = 90000
d = √(90000/8) = 75 √(2)
dmin = 75 √(2) ~ 106m
tmin = t(75 √(2)) = 100(4 + 3 √(2))/3 ~ 275 secs or 4 mins 35 secs
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