Carrie W.
asked • 01/12/15VELOCITY HELP!!!
A boat has a speed of 4ms−1 (relative to the surrounding water) and a
heading of 170?. There is a current flowing from a bearing of 105? at a
speed of 2.5ms−1. Take i to point east and j to point north.
heading of 170?. There is a current flowing from a bearing of 105? at a
speed of 2.5ms−1. Take i to point east and j to point north.
(a) Express the velocity U of the boat relative to still water and the
velocity w of the current in component form, giving numerical values
in ms−1 to one decimal place. [7]
velocity w of the current in component form, giving numerical values
in ms−1 to one decimal place. [7]
(b) Express the resultant velocity v of the boat in component form, giving
numerical values correct to one decimal place. [3]
(c) Hence find the magnitude and direction of the velocity v of the boat,
giving the magnitude to one decimal place in ms−1 and the direction
as a bearing to the nearest degree.
giving the magnitude to one decimal place in ms−1 and the direction
as a bearing to the nearest degree.
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1 Expert Answer
Mark M. answered • 01/12/15
Tutor
5.0
(278)
Mathematics Teacher - NCLB Highly Qualified
I noticed two errors that I made. Since i is the vector in the "x" direction it should be associated with "cos." And j should be associated with "sin."
And the current, w, is at 105° Sorry about that!
w = 2.5 cos 105° j + 2.5 sin 105° i
The numbers remain the same.
U = 4 cos (-80°)j + 4 sin (-80°)i
U = 4 (0.1736)j + 4 (-0.9840)i
U = 0.6944j – 0.3936i
The resulting direction of the boat is found by adding the vector components.
v = U + w
v = 0.6944j – 0.3936i + 1.75j - 1.75i
v = (0.6944 + 1.75)j + (-0.3936 – 1.75)i
v = 2.4444j – 2.1436i
Use the tangent function to find the direction.
Tan θ = -2.1436 / 2.444
And the current, w, is at 105° Sorry about that!
w = 2.5 cos 105° j + 2.5 sin 105° i
The numbers remain the same.
U = 4 cos (-80°)j + 4 sin (-80°)i
U = 4 (0.1736)j + 4 (-0.9840)i
U = 0.6944j – 0.3936i
The resulting direction of the boat is found by adding the vector components.
v = U + w
v = 0.6944j – 0.3936i + 1.75j - 1.75i
v = (0.6944 + 1.75)j + (-0.3936 – 1.75)i
v = 2.4444j – 2.1436i
Use the tangent function to find the direction.
Tan θ = -2.1436 / 2.444
Stumpils X.
hi
I think you resolved this around, I believe the vector for the boat is 4. Also why the -45 degree where is value from. I am also trying to resolve this exercise. Can you help with B and C
Thanks
Report
01/13/15
Mark M.
45° is the reference angles for 105° (105 - 90 = 45).
I noticed two errors that I made. Since i is the vector in the "x" direction it should be associated with "cos." And j should be associated with "sin."
And the current, w, is at 105° Sorry about that!
w = 2.5 cos 105° j + 2.5 sin 105° i
The numbers remain the same.
U = 4 cos (-80°)j + 4 sin (-80°)i
U = 4 (0.1736)j + 4 (-0.9840)i Calculate.
The resulting direction of the boat is found by adding the vector components.
v = U + w
I noticed two errors that I made. Since i is the vector in the "x" direction it should be associated with "cos." And j should be associated with "sin."
And the current, w, is at 105° Sorry about that!
w = 2.5 cos 105° j + 2.5 sin 105° i
The numbers remain the same.
U = 4 cos (-80°)j + 4 sin (-80°)i
U = 4 (0.1736)j + 4 (-0.9840)i Calculate.
The resulting direction of the boat is found by adding the vector components.
v = U + w
v = 0.6944j – 0.3936i + 1.75j - 1.75i
v = (0.6944 + 1.75)j + (-0.3936 – 1.75)i
v = 2.4444j – 2.1436i
Use the tangent function to find the direction.
Tan θ = -2.1436 / 2.444
v = (0.6944 + 1.75)j + (-0.3936 – 1.75)i
v = 2.4444j – 2.1436i
Use the tangent function to find the direction.
Tan θ = -2.1436 / 2.444
Report
01/13/15
Mark M.
I noticed two errors that I made. Since i is the vector in the "x" direction it should be associated with "cos." And j should be associated with "sin."
And the current, w, is at 105° Sorry about that!
w = 2.5 cos 105° j + 2.5 sin 105° i
The numbers remain the same.
U = 4 cos (-80°)j + 4 sin (-80°)i
U = 4 (0.1736)j + 4 (-0.9840)i
U = 0.6944j – 0.3936i
The resulting direction of the boat is found by adding the vector components.
v = U + w
v = 0.6944j – 0.3936i + 1.75j - 1.75i
v = (0.6944 + 1.75)j + (-0.3936 – 1.75)i
v = 2.4444j – 2.1436i
Use the tangent function to find the direction.
Tan θ = -2.1436 / 2.444
And the current, w, is at 105° Sorry about that!
w = 2.5 cos 105° j + 2.5 sin 105° i
The numbers remain the same.
U = 4 cos (-80°)j + 4 sin (-80°)i
U = 4 (0.1736)j + 4 (-0.9840)i
U = 0.6944j – 0.3936i
The resulting direction of the boat is found by adding the vector components.
v = U + w
v = 0.6944j – 0.3936i + 1.75j - 1.75i
v = (0.6944 + 1.75)j + (-0.3936 – 1.75)i
v = 2.4444j – 2.1436i
Use the tangent function to find the direction.
Tan θ = -2.1436 / 2.444
Report
01/13/15
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Mark M.
01/12/15