In order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are. 

Now lets identify what these values are.

To write this in component form, we need to put our , and  into .

So the final answer is 

Below is a visual representation of what we just did.

In order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are. 

Now lets identify what these values are.

To write this in component form, we need to put our , and  into .

So the final answer is 

Below is a visual representation of what we just did.

In order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are. 

Now lets identify what these values are.

To write this in component form, we need to put our , and  into .

So the final answer is 

Below is a visual representation of what we just did.

In order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are. 

Now lets identify what these values are.

To write this in component form, we need to put our , and  into .

So the final answer is 

Below is a visual representation of what we just did.

In order to figure this out, we need to create a picture.

Since bob is traveling south, and the current is traveling west, they are perpendicular to each other. This means that they are  to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed Bob is actually going. 

Recall that the Pythagorean Theorem is , where  is the hypotenuse, and ,  are the legs of the triangle, and  have a  angle between them.

For our calculations, let , and . 

In order to figure this out, we need to create a picture.

Since Amanda is traveling north, and the current is traveling east, they are perpendicular to each other. This means that they are  to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed Amanda is actually going. 

Recall that the Pythagorean Theorem is , where  is the hypotenuse, and ,  are the legs of the triangle, and  have a  angle between them.

For our calculations, let , and . 

Since the rock is going in the opposite direction of Jack, we simply subtract the speed of the rock from how fast Jack is going down the hill. 

In order to figure this out, we need to create a picture.

Since the airplane is traveling south, and the wind is coming from the west, they are perpendicular to each other. This means that they are  to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed the airplane is actually going. 

Recall that the Pythagorean Theorem is , where  is the hypotenuse, and ,  are the legs of the triangle, and  have a  angle between them.

For our calculations, let , and . 

Since the coin is going in the same direction as Jill, we simply add the speed of the coin and how fast Jill is going down the hill. 

Since Bob's wallet is going in the opposite direction, we simply subtract the speed of the wallet from how fast Bob is going down the hill.