- #1
Poppynz
- 6
- 0
Hi
Im trying to write an equation for the question below. Could someone please point me in the right direction with writing it?
An island is 4km from the nearest point p on the straight shoreline of a lake. if a person can row a boat at 3km/h and walk at 5km/h where should the boat be landed to arrive at a town 10km away is the least time?
I think the equation is y=(1/3)*(4^2+x^2)^(1/2)+((10-x)/5)
this doesn't look hard to differentiate but i can't seem to get the right answer-
in fact i get imaginary numbers
this is what i did
y=(1/3)*(16+x^2)^(1/2)-(1/5*x)+2
y'= -1/5+1/2*1/3(16+x^2)^(1/2)*2x
y'= -1/5+(2x/(6(16+x^2)^(1/2))
y'=0
1/5=x/(3(16+x^2)^(1/2))
3*(16+x^2)^(1/2)=5*x //square both sides
9*(16+x^2)=5*x^2
144+9x^2-5x^2=0
x= +/- 6i //this is obviously wrong as a person does not travel imaginary distances
Im trying to write an equation for the question below. Could someone please point me in the right direction with writing it?
Homework Statement
An island is 4km from the nearest point p on the straight shoreline of a lake. if a person can row a boat at 3km/h and walk at 5km/h where should the boat be landed to arrive at a town 10km away is the least time?
Homework Equations
The Attempt at a Solution
I think the equation is y=(1/3)*(4^2+x^2)^(1/2)+((10-x)/5)
this doesn't look hard to differentiate but i can't seem to get the right answer-
in fact i get imaginary numbers
this is what i did
y=(1/3)*(16+x^2)^(1/2)-(1/5*x)+2
y'= -1/5+1/2*1/3(16+x^2)^(1/2)*2x
y'= -1/5+(2x/(6(16+x^2)^(1/2))
y'=0
1/5=x/(3(16+x^2)^(1/2))
3*(16+x^2)^(1/2)=5*x //square both sides
9*(16+x^2)=5*x^2
144+9x^2-5x^2=0
x= +/- 6i //this is obviously wrong as a person does not travel imaginary distances
)
… you forgot to square the 5, so you got 5 - 9 instead of 25 - 9 