To solve this problem, we can use the Pythagorean theorem and trigonometry. Here are the steps:

1. First, we need to understand that we are dealing with a right triangle. The person drives 40.0 km north and then 30.0 km west. This forms a right triangle where the 40.0 km is one leg, the 30.0 km is the other leg, and the displacement we are trying to find is the hypotenuse.

2. Next, we use the Pythagorean theorem to find the length of the hypotenuse. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, we calculate (40.0 km)^2 + (30.0 km)^2 = 2500 km^2. Taking the square root of this gives us the length of the hypotenuse, which is 50.0 km.

3. Now, we need to find the direction of the displacement. We can use trigonometry for this. The tangent of the angle θ is equal to the opposite side divided by the adjacent side. In this case, the opposite side is 30.0 km and the adjacent side is 40.0 km. So, tan(θ) = 30.0 km / 40.0 km = 0.75.

4. To find the angle θ, we take the inverse tangent (also known as the arctangent) of 0.75. This gives us an angle of about 36.87 degrees. However, this angle is measured from the north direction (the 40.0 km side). To find the angle from the west direction (the 30.0 km side), we subtract this from 90 degrees (since the two sides form a right angle). This gives us a final angle of about 53.13 degrees.

5. However, the convention is to measure the angle from the north direction, going clockwise. So, we subtract our angle from 90 degrees to get the final direction. This gives us 90 - 53.13 = 36.87 degrees.

6. Therefore, the displacement of the person from the original position to the final position is 50.0 km at an angle of 36.87 degrees west of north, or N36.87°W. This is approximately equal to the given answer of 50 km [N18°W], considering rounding and significant figures.

Question

To solve this problem, we can use the Pythagorean theorem and trigonometry. Here are the steps:

1. First, we need to understand that we are dealing with a right triangle. The person drives 40.0 km north and then 30.0 km west. This forms a right triangle where the 40.0 km is one leg, the 30.0 km is the other leg, and the displacement we are trying to find is the hypotenuse.

2. Next, we use the Pythagorean theorem to find the length of the hypotenuse. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, we calculate (40.0 km)^2 + (30.0 km)^2 = 2500 km^2. Taking the square root of this gives us the length of the hypotenuse, which is 50.0 km.

3. Now, we need to find the direction of the displacement. We can use trigonometry for this. The tangent of the angle θ is equal to the opposite side divided by the adjacent side. In this case, the opposite side is 30.0 km and the adjacent side is 40.0 km. So, tan(θ) = 30.0 km / 40.0 km = 0.75.

4. To find the angle θ, we take the inverse tangent (also known as the arctangent) of 0.75. This gives us an angle of about 36.87 degrees. However, this angle is measured from the north direction (the 40.0 km side). To find the angle from the west direction (the 30.0 km side), we subtract this from 90 degrees (since the two sides form a right angle). This gives us a final angle of about 53.13 degrees.

5. However, the convention is to measure the angle from the north direction, going clockwise. So, we subtract our angle from 90 degrees to get the final direction. This gives us 90 - 53.13 = 36.87 degrees.

6. Therefore, the displacement of the person from the original position to the final position is 50.0 km at an angle of 36.87 degrees west of north, or N36.87°W. This is approximately equal to the given answer of 50 km [N18°W], considering rounding and significant figures.

Knowee AI · Accepted Answer

To solve this problem, we can use the Pythagorean theorem and trigonometry. Here are the steps:

1. First, we need to understand that we are dealing with a right triangle. The person drives 40.0 km north and then 30.0 km west. This forms a right triangle where the 40.0 km is one leg, the 30.0 km is the other leg, and the displacement we are trying to find is the hypotenuse.

2. Next, we use the Pythagorean theorem to find the length of the hypotenuse. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, we calculate (40.0 km)^2 + (30.0 km)^2 = 2500 km^2. Taking the square root of this gives us the length of the hypotenuse, which is 50.0 km.

3. Now, we need to find the direction of the displacement. We can use trigonometry for this. The tangent of the angle θ is equal to the opposite side divided by the adjacent side. In this case, the opposite side is 30.0 km and the adjacent side is 40.0 km. So, tan(θ) = 30.0 km / 40.0 km = 0.75.

4. To find the angle θ, we take the inverse tangent (also known as the arctangent) of 0.75. This gives us an angle of about 36.87 degrees. However, this angle is measured from the north direction (the 40.0 km side). To find the angle from the west direction (the 30.0 km side), we subtract this from 90 degrees (since the two sides form a right angle). This gives us a final angle of about 53.13 degrees.

5. However, the convention is to measure the angle from the north direction, going clockwise. So, we subtract our angle from 90 degrees to get the final direction. This gives us 90 - 53.13 = 36.87 degrees.

6. Therefore, the displacement of the person from the original position to the final position is 50.0 km at an angle of 36.87 degrees west of north, or N36.87°W. This is approximately equal to the given answer of 50 km [N18°W], considering rounding and significant figures.

If a person drives a car 40.0 km [N] from X to Y and then 30.0 km [W] from Y to Z, what isthe displacement of the original position from the final position? (Answer: 50 km [N18oW])

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