# In an explosion, a piece of debris is tossed 99 meters N 45 W. what is the displacement in the north and west directions. I'm not really sure what it wants when it asks for displacement so I also don't know how to get it.

## N45W ---> an angle of 135° using trig notation.

So we are de-composing your vector into its vertical and horizontal displacement.
horizontal: 99cos 135
= 99(-√2/2) = appr - 70 metres
vertical : 99 sin 135° = appr 70 metres

notice if you construct a right-angled triangle in the 2nd quadrant having an angle of 135° and a hypotenuse of 99 metres, the height can be found:
h/99 = sin135 ----> h = 99sin135 = appr 70
the base is :
b/99 = cos135 ----> b = 99cos 135 = appr -70
the ordered pair of the end of the hypotenuse is about (-70, 70)

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## To find the displacement in the north and west directions, we need to break down the given distance into its components.

In this case, the debris is tossed 99 meters N 45 W.

"N" represents north and "W" represents west.

Using the information provided, we can break down the distance into its north and west components using trigonometry.

The north component can be found by multiplying the given distance (99 meters) by the cosine of the angle between north and the direction of the debris. Since the angle between north and 45 degrees west is 45 degrees, we have:

North component = 99 meters * cos(45°)

The west component can be found by multiplying the given distance (99 meters) by the sine of the angle between west and the direction of the debris. Since the angle between west and 45 degrees west is 0 degrees, we have:

West component = 99 meters * sin(0°)

Calculating these values, we get:

North component = 99 meters * cos(45°) ≈ 70.14 meters north
West component = 99 meters * sin(0°) = 0 meters west

Therefore, the displacement in the north direction is approximately 70.14 meters north, and there is no displacement in the west direction.

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## Displacement refers to the change in position of an object. In this case, we need to determine the displacement in the north and west directions of the piece of debris.

To calculate the displacement, we need to break down the toss distance of the debris into its north and west components. The given values, 99 meters and an angle of 45 degrees west of north, can be used to find these components.

Let's start by determining the north displacement. Since the debris is tossed in the northwest direction, the north component of the displacement is the length of the side opposite to the given angle of 45 degrees. By using trigonometry, we can find this value.

Using the trigonometric function sine (sin), we have:

North displacement = 99 meters * sin(45°)

Plugging the values into a calculator, we find:

North displacement ≈ 99 meters * 0.7071 ≈ 69.693 meters

Therefore, the north displacement is approximately 69.693 meters.

Next, we'll find the west displacement. Similar to the north displacement, the west component is the length of the side adjacent to the given angle. We can use the trigonometric function cosine (cos) to determine this value.

Using cosine, we have:

West displacement = 99 meters * cos(45°)

Calculating this using a calculator, we find:

West displacement ≈ 99 meters * 0.7071 ≈ 69.693 meters

Thus, the west displacement is approximately 69.693 meters as well.

To summarize:

- The displacement in the north direction is approximately 69.693 meters.
- The displacement in the west direction is also approximately 69.693 meters.

Therefore, the displacement of the piece of debris in the north and west directions is approximately 69.693 meters both ways.