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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 inland (see figure). 3-x (a) The man rows at 1 mile per hour and walks at 2 miles per hour. Toward what point on the coast 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 v, miles per hour and walks at v2 miles per hour. Let 0, and 0, be the magnitu sin(0,) sin(02) Show that the man will reach point Q in the least time when V1 V2 Write the equation for time in terms of x, v, and v2. t = Write the equation for the derivative of time in terms of x, V1, and v2. dt dx Write the equations for sin(0,) and sin(0,) in terms of x.

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 inland (see figure). 3-x (a) The man rows at 1 mile per hour and walks at 2 miles per hour. Toward what point on the coast 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 v, miles per hour and walks at v2 miles per hour. Let 0, and 0, be the magnitu sin(0,) sin(02) Show that the man will reach point Q in the least time when V1 V2 Write the equation for time in terms of x, v, and v2. t = Write the equation for the derivative of time in terms of x, V1, and v2. dt dx Write the equations for sin(0,) and sin(0,) in terms of x.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 68E
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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 inland (see figure). 3- X (a) The man rows at 1 mile per hour and walks at 2 miles per hour. Toward what point on the coast she 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 v, miles per hour and walks at v, miles per hour. Let 0, and 0, be the magnitude sin(0,) sin(02) Show that the man will reach point Q in the least time when V1 V2 Write the equation for time in terms of x, v,, and v,. t = Write the equation for the derivative of time in terms of x, v,, andv,. dt dx Write the equations for sin(0,) and sin(0,) in terms of x. sin(0,) = sin(82) = By substituting sin(0,) and sin(0,) into the equation for - dt we have: dx dt sin(0,) sin(0,) sin(0,) sin(0,) dx V1 V2 V1 V2 Write the equation for the second derivative of time in terms of x, v,, and v,. d?t %3D dx2 d?t Since dx2 0, this condition yields a minimum time. Nood Holn? Wetsh
Transcribed Image Text: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 inland (see figure). 3- X (a) The man rows at 1 mile per hour and walks at 2 miles per hour. Toward what point on the coast she 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 v, miles per hour and walks at v, miles per hour. Let 0, and 0, be the magnitude sin(0,) sin(02) Show that the man will reach point Q in the least time when V1 V2 Write the equation for time in terms of x, v,, and v,. t = Write the equation for the derivative of time in terms of x, v,, andv,. dt dx Write the equations for sin(0,) and sin(0,) in terms of x. sin(0,) = sin(82) = By substituting sin(0,) and sin(0,) into the equation for - dt we have: dx dt sin(0,) sin(0,) sin(0,) sin(0,) dx V1 V2 V1 V2 Write the equation for the second derivative of time in terms of x, v,, and v,. d?t %3D dx2 d?t Since dx2 0, this condition yields a minimum time. Nood Holn? Wetsh
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