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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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
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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