6. A woman takes her dog Rover for a walk on a leash. To get the little poco moving forward, she pulls on the leash with a force of 20.0 N at an angle of 37 degrees above the horizonta. How much force is tending to lift Rover off the ground?
16.0 N
12.0 N
20.0 N
42.1 N

10. Vector A has a magnitude of 12.6 m and a direction of -84.0 degrees. Vector B ha a a magnitude of 34.0 m and a direction of -75.0 degrees. What is the resultant magnitude and direction of a vector that is equal to A+B?
Magnitude 20.6 m Direction -71.1 degrees
Magnitude 46.4 m Direction -77 degrees
Magnitude 20.6 m Direction -78.2 degrees
Magnitude 46.4 m Direction 102 degrees

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aristocles aristocles · Answer 1 · 2018-09-20T01:48:26+02:00

#6

woman applies a force of 20 N at an angle of 37 degree from the ground

So here the two components of force is given as

[tex]F_x = 20 cos37 = 16 N[/tex]

[tex]F_y = 20 sin37 = 12 N[/tex]

so here the vertical force on the dog that pull it off the ground is 12 N

So correct answer here is 12 N

#10

vector A is 12.6 at angle of -84 degree

vector B is 34 at angle -75 degree

now we can write

[tex]\vec A = 12.6 cos-84\hat i + 12.6sin-84 \hat j[/tex]

[tex]/vec A = 1.32 \hat i - 12.5\hat j[/tex]

[tex]\vec B = 34 cos-75 \hat i + 34 sin-75[/tex]

[tex]\vec B = 8.8 \hat i - 32.8\hat j[/tex]

[tex]\vec A + \vec B = (8.8 + 1.32)\hat i - (12.5 + 32.8)\hat j[/tex]

[tex]\vec A + \vec B = 10.12 \hat i - 45.3 \hat j[/tex]

magnitude = 46.42

direction = [tex]tan^{-1}\frac{-45.3}{10.12}[/tex]

direction = -77.4 degree

so correct answer is

Magnitude 46.4 m Direction -77 degrees