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) (a) The man rows at 2 miles per hour and walks at 4 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.) mile(s) down the coast (b) The man rows at vi miles per hour and walks at v2 miles per hour. Let θ1 and θ2 be the magnitudes of the angles. Show that the man will reach point Q in the least time when Sin(^1inG. Write the equation for time in terms of x, v, and V2 Write the equation for the derivative of time in terms of x, v dt άκ and v2 Write the equations for sin(1) and sin(82) in terms of x sin(1 sin(82) By substituti) and sin(e2) into the equation for dt dx we have since, sin(θ2) write the equation for the second derivative of time in terms of x, v1, and v2 d't dx 2 d-t Since ?0, this condition yields a minimum time Need Help?Read It Watch It Talk to a Tutor Submit Answer Save Progress Practice Another Version

Answer 1

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