To Evaluate: Expression of river velocity in component form, expression of velocity of motorboat relative to water in component form, true velocity of motorboat as a
Answer to Problem 63E
The expression of river velocity in component form is
Explanation of Solution
Given:
The speed of river is
The speed of motorboat is
The speed of river is
Formula used:
If velocity of river is vector u which makes angle
If velocity of motorboat is vector v which makes angle
If vector u is
Calculation:
The speed of river is
The angle made by river velocity with positive
River velocity vector u is shown on coordinate axis in Figure (1).
Figure (1)
Substitute
Thus, component form of river velocity u is
Obtain the component form of motorboat velocity.
The speed of motorboat is
Velocity of motorboat is shown in Figure (2).
Figure (2)
Substitute
Thus, component form of motorboat velocity u is
Obtain the true velocity of motorboat.
If true velocity of motorboat is vector p , then vector p will be the resultant sum of river velocity u and velocity v of motorboat.
Figure (3) shows the vector u, vector v and vector p on coordinate axis.
Figure (3)
From section(a) river velocity u is
Substitute
And vector p is
Therefore,
Thus true velocity of motorboat is
From Section(c), the true velocity of motorboat is
Substitute
Therefore, true speed of motorboat is
If
angle
From section (c), true velocity vector of motorboat is
Thus,
Solve for
So, direction is
Therefore true speed of motorboat is
Chapter 9 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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