A man in a rowboat at p, see fig 2c, 5km from the nearest point A on the straight shore. He wished to reach a point B, 6km from A along the shore, in a shortest time. Where should he land if he can row 2km/h and walks 4km/h?
P
5 km
A C B
4 answers
Unfortunately we cannot see fig 2c unless you describe it or send a link.
i cant attach the triangle...
If this is a typical problem, then if he lands at a distance x from A, then the distance on water is
√(x^2+5^2)
and the distance on land is 6-x
So, the time taken is
t = √(x^2+25)/2 + (6-x)/4
dt/dx = x / 2√(x^2+25) - 1/4
= (2x-√(x^2+25)) / 4√(x^2+25)
dt/dx=0 when x=5/√3
at that point, the minimum t = (6+5√3)/4
√(x^2+5^2)
and the distance on land is 6-x
So, the time taken is
t = √(x^2+25)/2 + (6-x)/4
dt/dx = x / 2√(x^2+25) - 1/4
= (2x-√(x^2+25)) / 4√(x^2+25)
dt/dx=0 when x=5/√3
at that point, the minimum t = (6+5√3)/4
Don't get it ?? Help!!
1 answer