Answer to Question #171106 in Physics for Gail

Question

1. A jogger runs 300 meters due east and then 500 meters due south. 

What is the total distance that she ran? (2 mks)

What is her total displacement (magnitude and direction)? (4 mks)

1.  A plane flying due north at 2000 msᐨ¹ encounters winds which blow the plane due south at 45 msᐨ¹.

Determine the plane's resultant velocity (magnitude and direction). (4 mks)

1. Two ropes are attached to a heavy object. The ropes are given to two strong women with instructions to pull with exactly 1000N of force. What is the magnitude of the resultant force on the object if the two women pull:

in the same direction (2 mks)

in opposite directions (2 mks)

at right angles to each other (3 mks)

1. A dog's owner walks 20 meters due west and then walks north a distance of 150 meters.

Where is he with respect to where he started? (3 mks)

1. You push on a box with a force of 500 N directly east.  Another person pushes the box with a force of 800 N directly west.  What is the resultant force?    (2 mks)

Answer 1

1. The total distance:

$$D=300+500=800\text{ m}.$$

Displacement (magnitude):

$$d=\sqrt{300^2+500^2}=583\text{ m}.$$

Direction:

$$\theta=\text{atan}\frac{500}{300}=59°$$

South of East.

1. Resultant if pull in the same direction:

$$R=1000+1000=2000\text{ N}.$$

Pull in opposite directions:

$$R=1000-1000=0.$$

Pull and there is an angle $\alpha$ between the forces:

$$R=1000+1000\text{ cos}\alpha=1000(1+\text{cos}\alpha).$$

1. With respect to where he started, he is

$$d=\sqrt{20^2+150^2}=151.3\text{ m}$$

away.

1. The resultant force is

$$R=800-500=300\text{ N}$$

toward the action of 800N-force.