You are camping with Joe and Karl. Since all three of you like your privacy, you don’t pitch your tents close together. Joe’s tent is 21.0 m from yours, in the direction $23.0^{\circ}$ south of east. Karl’s tent is 32.0 m from yours, in the direction $37.0^{\circ}$ north of east. What is the distance between Karl’s tent and Joe’s tent?

A plane leaves the airport in Galisteo and flies 170 km at $68.0^{\circ}$ east of north; then it changes direction to fly 230 km at $36.0^{\circ}$ south of east, after which it makes an immediate emergency landing in a pasture. When the airport sends out a rescue crew, in which direction and how far should this crew fly to go directly to this plane?

For what values of a is each statement true? Give an example, if possible.

$$| a - 5 | = | a | - 5$$

A charged object with electric charge q produces an electric field. The SI unit for electric field is N/C, where N is the SI unit for force and C is the SI unit for charge. If at point P there are electric fields from two or more charged objects, then the resultant field is the vector sum of the fields from each object. At point P the electric field $\vec{E}_{1}$ from charge $q_{1}$ is 450 N/C in the +y-direction, and the electric field $\vec{E}_{2}$ from charge $q_{2}$is 600 N/C in the direction 36.9$^\circ$ from the -y-axis toward the -x-axis. What are the magnitude and direction of the resultant field $\vec{E}=\vec{E}_{1}+\vec{E}_{2}$ at point P due to these two charges?

Forces $\vec { F _ { 1 } }$ and $\vec { F _ { 2 } }$ act at a point. The magnitude of $\vec { F _ { 1 } }$ is 9.00 N, and its direction is $60.0 ^ { \circ }$ above the x-axis in the second quadrant. The magnitude of $\vec { F _ { 2 } }$ is 6.00 N, and its direction is $53.1 ^ { \circ }$ below the x-axis in the third quadrant. (a) What are the x- and y-components of the resultant force? (b) What is the magnitude of the resultant force?

You are a delivery person for the Fresh Aqua Spring Water Company. Your truck carries 4 pallets. Each pallet carries 60 cases of water. Each case of water has 24 one-liter bottles. The dolly you use to carry the water into the stores has a weight limit of $250 \mathrm{lb}$.

(b) How many full cases of water can you carry on the cart?

As a test of orienteering skills, your physics class holds a contest in a large, open field. Each contestant is told to travel 20.8 m due north from the starting point, then 38.0 m due east, and finally 18.0 m in the direction $33.0^{\circ}$ west of south. After the specified displacements, a contestant will find a silver dollar hidden under a rock. The winner is the person who takes the shortest time to reach the location of the silver dollar. Remembering what you learned in class, you run on a straight line from the starting point to the hidden coin. How far and in what direction do you run?

A dog in an open field runs 12.0 m east and then 28.0 m in a direction $50.0^{\circ}$ west of north. In what direction and how far must the dog then run to end up 10.0 m south of her original starting point?

A stone is thrown into the air at an angle above the horizontal and feels negligible air resistance. Which graph in the given figure best depicts the stone’s speed as a function of time t while it is in the air?

Ricardo and Jane are standing under a tree in the middle of a pasture. An argument ensues, and they walk away in different directions. Ricardo walks 26.0 m in a direction $60.0^{\circ}$ west of north. Jane walks 16.0 m in a direction $30.0^{\circ}$ south of west. They then stop and turn to face each other. (a) What is the distance between them? (b) In what direction should Ricardo walk to go directly toward Jane?

Prove that $b \; | \; a$ if and only if $(-b) \; | \; a$.

Solve the proportion.

$$\frac { 5 } { 4 } = \frac { 10 } { x }$$

A man pushing a mop across a floor causes it to undergo two displacements. The first has a magnitude of 150 cm and makes an angle of $120 ^ { \circ }$ with the positive x axis. The resultant displacement has a magnitude of 140 cm and is directed at an angle of $35.0 ^ { \circ }$ to the positive x axis. Find the magnitude and direction of the second displacement.

The scalar product of vectors $\vec{A}$ and $\vec{B}$ is $+48.0 m^{2}$. Vector $\vec{A}$ has magnitude 9.00 m and direction $28.0^{\circ}$ west of south. If vector $\vec{B}$ has direction $39.0^{\circ}$ south of east, what is the magnitude of $\vec{B}$.