Find the resultant displacement of a bear searching for berries on the mountain. The bear heads 55.0º north of west for 15.0 m; then it turns and heads to the west for another 7.00 m. (Use trigonometry to answer, but remember to draw a diagram to help your understanding.) Give both the magnitude and the angle in your answer.
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Hi Welcome to OpenStudy @13whitneyh
First, you have to draw a diagram:
To solve for the resultant displacement: you can resolve the 15 m vector into components, x and y.
Since the x component of the 15 m vector has the same direction with the 7m horizontal vector, you just have to add them.
Rx= 15 cos (55) + 7
Since 7m vector only lies on the horizontal, it means that your Ry will only be the y-component of the 15 m vector:
Once you find those two values, you can easily find the Resultant vector using the Pythagorean theorem :)
When dealing with vectors in 2D, always remember that each vector has two components, x and y. These components help us calculate how far an object has moved horizontally on x-axis (E-W) or Vertically (N-S) on the y-axis. Since we have a scenario that involves 2 vectors, we're gunna have 4 components in total. Let's see how we tackle the problem.
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Since we have two vectors, we're going to have two x components and 2 y components. For your ease the formula shows which x components you're dealing with. In this case Delta x1 is the initial displacement from the origin and Delta x 2 is the second displacement where the first one ended. The total distance bear covered on the horizontal axis is 15.60m going towards the [W] |dw:1435437134492:dw|
To figure out how much distance the bear covered on the y-axis or horizontally. We 're going to use the same formula but a different tri-identity. This time it's gunna be Sin |dw:1435438027616:dw|
Now that you have your x and y components, Draw a separate right triangle to make things easier for yorself and use the Pythagorean theorem to figure out the longest side.|dw:1435439667139:dw|
To determine the angle.......use Tan0 = Total vertical displacement/ total horizontal displacement. Take the inverse of tan and you should get 38.28 Degress. Your full anser wold look something like this..... 19.85m(N38W)