A man is in a boat 2 miles from the nearest point on the coast. He is to go to p
ID: 2840957 • Letter: A
Question
A man is in a boat 2 miles from the nearest point on the coast. He is to go to point Q, located 3 miles down the coast and 1 mile inland (see figure). He can row at a rate of 2 miles per hour and walk at 3 miles per hour. Toward what point on the coast should he row in order to reach point Q in the least time? (Round your answer to two decimal places.)
A man is in a boat 2 miles from the nearest point on the coast. He is to go to point Q, located 3 miles down the coast and 1 mile inland (see figure). He can row at a rate of 2 miles per hour and walk at 3 miles per hour. Toward what point on the coast should he row in order to reach point Q in the least time? (Round your answer to two decimal places.)Explanation / Answer
time taken to reach coast = (sqrt(2^2 + x^2))/2
time taken to reach Q after reaching coast = (sqrt(1 + (3-x)^2))/3
Total time, T = (sqrt(2^2 + x^2))/2 + (sqrt(1 + (3-x)^2))/3
This has to be minimum,
Dt/dx = 0
x/2sqrt(4+x^2) + (x-3)/(3sqrt(x^2-6x+10)) = 0
x^2/4*(4+x^2) = (x-3)^2/9*(x^2-6x+10)
4(4+x^2)(x-3)^2 = 9*(x^2-6x+10)*x^2
5x^4 - 30x^3 + 110x^2 + 96x - 144 = 0
x = 0.844 miles
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.