If the Queen Bee leaves the hive and travels 210 m [N32°E] and then 37 m [S51°W], how far and in what direction is the bee from its hive? I am unsure of my final answer, can someone please explain this so I know if I am doing this right? THANKS!
I made a diagram and obtained a triangle with sides 37 and 210 with a 19ºbetween them
Using the cosine law if found the side opposite the 19º angle to be 175.4
So the bee is 175.4 m from the hive
Then using the sine law I got the angle between the resultant and the first path to be 3.9º
so its direction would be 28.1º
WOuld the direction be [N28E]? I think I need to give the compass bearings. But thanks so much, I did do the same steps as you, but my overall direction is [N28E]? Do you agree? Thanks, again~
Yes, it would be N28.1ºE or rounded off to the nearest degree like you appear to have done.
Good job.
THANKS!!! You ROCK!!!
To find the final distance and direction of the bee from its hive, we can use vector addition.
Step 1: Draw a diagram
- Draw a coordinate system where the hive is located at the origin (0, 0).
- From the origin, draw a vector 210 m [N32°E] (north 32 degrees east). This vector represents the bee's first movement.
- From the end of this vector, draw a second vector 37 m [S51°W] (south 51 degrees west). This vector represents the bee's second movement.
- Connect the origin with the end of the second vector to complete the triangle.
Step 2: Break down the vectors into their components
- To break down the vectors into their horizontal (x) and vertical (y) components, we can use trigonometry.
- The first vector (210 m [N32°E]) can be broken down into two components: 210 * cos(32°) in the x-direction and 210 * sin(32°) in the y-direction.
- The second vector (37 m [S51°W]) can be broken down into two components: 37 * cos(51°) in the x-direction and 37 * sin(51°) in the y-direction.
Step 3: Find the sum of the x and y components
- Add up the x-components of the two vectors and separately add up the y-components of the two vectors.
Step 4: Use the sum of the x and y components to find the magnitude and direction
- The magnitude is given by the equation sqrt((sum of x-components)^2 + (sum of y-components)^2).
- The direction can be found using the inverse tangent function. The angle θ is given by tan^(-1)(sum of y-components / sum of x-components).
By following these steps, you should be able to find the final distance and direction of the bee from its hive.