An elephant walks east for a distance of 30 km, then walks north for a distance of 16 km and finally north east at 300 for 18 km. Find the magnitude of the elephant’s total displacement in kilometers.
Please explain how I would do this problem? Do I add all of the numbers once i find the sine and cosine?
northeast is not 300 degrees. It is 45. what are you talking about ?
To find the magnitude of the elephant's total displacement, you need to calculate the resultant displacement, which is the straight-line distance from the starting point to the final location. You can find the resultant displacement using the Pythagorean theorem.
Here's how you can solve the problem step by step:
1. Start by breaking down the elephant's motion into its east-west (x-axis) and north-south (y-axis) components.
- The elephant walks east for 30 km, which means it has an eastward displacement of +30 km.
- The elephant then walks north for 16 km, resulting in a northward displacement of +16 km.
- Lastly, the elephant moves northeast at 45 degrees for 18 km. To find the x and y components, you can decompose the displacement into its east-west and north-south components using trigonometry:
- The east-west component is given by cos(45°) × 18 km, which is approximately 12.73 km.
- The north-south component is given by sin(45°) × 18 km, which is also approximately 12.73 km.
2. Add up the east-west and north-south components to find the resultant displacement.
- The total east-west displacement is 30 km + 12.73 km = 42.73 km.
- The total north-south displacement is 16 km + 12.73 km = 28.73 km.
3. Use the Pythagorean theorem to find the magnitude of the displacement.
- The magnitude of the resultant displacement (R) is given by R = √[(east-west)^2 + (north-south)^2].
- In this case, R = √[(42.73 km)^2 + (28.73 km)^2].
- Calculate the square of each component, then add them together, and finally take the square root of the sum to get the magnitude of the displacement.
So, by evaluating the above expression, you will be able to determine the magnitude of the elephant's total displacement in kilometers.