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3 Problems related to Vectos: Force, Motion, currents

Please explain in step by step detail the following:
25. A weight of 850 pounds is suspended by two cables. One cable makes an angle of 66 degrees with a vertical line, the other makes an angle of 42 degrees with a vertical line. Find the amount of force exerted by each of the cables.

24. An airplane is scheduled to reach an airport 600 miles away in exactly 3 hours. If the airport is directly northeast of the starting point and a wind of 20 mph will be forcing the plane southward, at what angle should the pilot head the plane? What should the air speed be?

23. The resultant of two currents of electricity is 12 amperes at a direction angle of 30 degrees. If one of the currents consists of 15 amperes at 60 degrees ( from what would be the positive x axis), what is the vector of the other current?

On the above please explain resultant, vector, and formulas used.

Solution Preview

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25. A weight of 850 pounds is suspended by two cables. ONe cable makes an angle of 66 degrees with a vertical line, the other makes an angle of 42 degrees with a vertical line. Find the amount of force exerted by each of the cables.

Please give all formulas used.

Answer:

The force exerted by the cable is due to the tension in the cables.
Let the tensions in the cables or the force exerted by the cables are F1 and F2 in magnitude, the directions are given. The two forces balance the weight of the body suspended, means that the resultant of F1, F2 and W must be zero.

Force is a vector quantity and to find the resultant of number of vectors, we write them in components form and then add the components in each direction algebraically. Here i and j are unit vectors in x and y directions respectively.

If vector A makes an angle θ with ...

Solution Summary

The solution assists with explaining the equilibrium of forces, the motion of airplane in presence of wind and electric currents.

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