Expert: Paul Klarreich - 8/24/2009

Question
three forces with magnitudes 70 pounds, 40 pounds, and 60 pounds act on an object at angles of -30 degrees, 45 degrees, and 135 degrees, respectively with positive x-axis. Find the direction and magnitude of the reluctant of these forces.

use the Law of Cosines to find the angle theta between the given vectors. (Assume 0 degree <=theta<=180degrees)v= i+ j, w=2(i - j)

an airplane's velocity with respect to the air is 580 miles per hour, and it is heading N 60 degrees W. The wind, at the altitude of the lane, is from the southwest and has a velocity of 60 miles per hour. Draw a figure that gives a visual representation of the problem. What is the true direction of the plane, and what is its speed with respect to the ground?.


I have no idea what to do these problems. Thank you for your help!

Answer
Questioner: Nelson
Country: United States
Category: Advanced Math
Private: No
Subject: Pre-Cal problems
Question: three forces with magnitudes 70 pounds, 40 pounds, and 60 pounds act on an object at angles of -30 degrees, 45 degrees, and 135 degrees, respectively with positive x-axis. Find the direction and magnitude of the reluctant of these forces.

use the Law of Cosines to find the angle theta between the given vectors. (Assume 0 degree <=theta<=180degrees)v= i+ j, w=2(i - j)

an airplane's velocity with respect to the air is 580 miles per hour, and it is heading N 60 degrees W. The wind, at the altitude of the lane, is from the southwest and has a velocity of 60 miles per hour. Draw a figure that gives a visual representation of the problem. What is the true direction of the plane, and what is its speed with respect to the ground?.


I have no idea what to do these problems. Thank you for your help!
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This is a lot, so I will get you started on each one and let you finish up.  (That is all I am allowed to do.  This is not a do-your-homework-for-you site; they have strict rules about that).

Question: three forces with magnitudes 70 pounds, 40 pounds, and 60 pounds act on an object at angles of -30 degrees, 45 degrees, and 135 degrees, respectively with positive x-axis. Find the direction and magnitude of the reluctant
>> (I think that word is RESULTANT)
of these forces.

For each one of the three forces, find the x- and y-components.  Use

x = M cos t
y = M sin t

where M is the magnitude, t (theta) is the angle in std pos.

Then add your x's, add your y's and you have your components of the resultant.  Finally you can get  M from the pythagorean theorem, and theta from your basic trigonometry.

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use the Law of Cosines to find the angle theta between the given vectors. (Assume 0 degree <=theta<=180degrees)v= i+ j, w=2(i - j)

Since you have to use L.of C., (not my choice) find:

a. length(v) = a
b. length(w) = b
c. length of vector between (1,1), (2,-2) = c.  (use the distance formula.)

Now use:

c^2 = a^2 + b^2 - 2ab cos C, and solve for C.

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an airplane's velocity with respect to the air is 580 miles per hour, and it is heading N 60 degrees W. The wind, at the altitude of the lane, is from the southwest and has a velocity of 60 miles per hour. Draw a figure that gives a visual representation of the problem. What is the true direction of the plane, and what is its speed with respect to the ground?.


You will have to draw it yourself.  But you can find the vertical (y) and horizontal (x) components of each velocity and add them.  Then use the same relations as in the first problem (resultant) to find your speed and angle.