Vectors

[Guest]

Can someone help solve these problems, I am really stuck on them.


Bob’s car stalled as he was driving up an incline that makes an angle of 15° with the horizontal. If the car weighs 4500 pounds, find the magnitude of the force that pulls his car down the incline.

If two forces with an angle of 60° between them have a resultant of 100 N and one of the forces is 80 N, find the other force (to the nearest tenth of a Newton) and the angle the unknown force makes with the resultant. Draw a sketch.

A plane is traveling due west with an air speed of 400 miles per hour. There is a tailwind blowing from the northeast with a bearing of 225° at 50 miles per hour. Use the drawing below to determine the direction and the magnitude of the groundspeed of the plane.

Two forces with, 1 F and 2 F , with magnitudes of 20N and 30N respectively, act on an object at point P. 1 F angle is 45 degrees and 2 F angle is 150 degrees. Determine the resultant force, F , in component form.


I appreciate your help in advance. My professors notes had nothing to do with these problems and after watching several videos on vectors I am left feeling more confused than ever

[Guest]

Saying that you are "stuck" implies that you have tried something on these problems! Why haven't you shown what you have tried?

The first problem asks you to write the force vector 4500 pounds as a sum of a vector perpendicular to the surface and a vector parallel to the surface. 4500 can be thought of as the length of the hypotenuse of a right triangle with angle 15 degrees and 75 degrees. Use trig functions to determine the length of the two legs.

For the second problem you have triangle with lengths of two sides of a triangle with angle between them 60 degrees. Use the "law of cosines" (https://en.wikipedia.org/wiki/Law_of_cosines) to find the length of the third side, then use the "law of sines"(https://en.wikipedia.org/wiki/Law_of_sines), to find the other two angles.

The third problem is similar. Adding the vectors "tail to head" gives two sides of a triangle, of lengths 400 and 50 with angle between them 180-(270- 225)= 135 degrees. Use the law of cosines to find the length of the third side (the length of the resultant vector) and the law of sines to find the direction.

The fourth problem is the same: use the law of cosines and law of sines.