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

20 *sin 37

is a little more than 20 sin 30 which would be 10

Ax = 12.6 cos 84

Ay = -12.6 sin 84

Bx = 34 cos 75
By = -34 sin 75

Rx = Ax+Bx
Ry = Ay+By
R = sqrt (Rx^2+Ry^2)
angle = tan^-1 (Ry/Rx)
HOWEVER USE HEAD instead
both are almost in the same direction
so
magnitude is a little less than 12.6+34
and direction is between - 75 and -84
SO
around 47 at angle about -80
only one answer is close :)

So is 6, 12.0 N and 10. 46.4 and -77 degrees?

yes, yes

To find the force tending to lift Rover off the ground, we need to determine the vertical component of the force applied to the leash. To do this, we can use trigonometry.

The vertical component of the force can be found by multiplying the force applied (20.0 N) by the sine of the angle of 37 degrees:

Vertical component = (20.0 N) * sin(37 degrees) = 12.0 N

Therefore, the force tending to lift Rover off the ground is 12.0 N.

For the second question, to find the resultant magnitude and direction of a vector that is equal to A + B, we can use vector addition.

First, we need to break down vectors A and B into their horizontal and vertical components using trigonometry.

Vector A:
Magnitude = 12.6 m
Direction = -84.0 degrees
Horizontal component = magnitude * cos(direction) = 12.6 m * cos(-84.0 degrees)
Vertical component = magnitude * sin(direction) = 12.6 m * sin(-84.0 degrees)

Vector B:
Magnitude = 34.0 m
Direction = -75.0 degrees
Horizontal component = magnitude * cos(direction) = 34.0 m * cos(-75.0 degrees)
Vertical component = magnitude * sin(direction) = 34.0 m * sin(-75.0 degrees)

Next, we add up the horizontal components and the vertical components separately:

Resultant horizontal component = Horizontal component of Vector A + Horizontal component of Vector B
Resultant vertical component = Vertical component of Vector A + Vertical component of Vector B

Finally, we can use the magnitude and direction of the resultant vector using the Pythagorean theorem and trigonometry:

Resultant magnitude = √(Resultant horizontal component^2 + Resultant vertical component^2)
Resultant direction = arctan(Resultant vertical component / Resultant horizontal component)

By plugging in the calculated values into these formulas, we can find the resultant magnitude and direction of the vector that is equal to A + B.