How Do You Calculate a Drunk Skunk's Displacement?

[ryant14]

Homework Statement

In the figure below shows the path taken by a drunk skunk over a level ground, from initial point i to final point f. The angles are θ₁ = 30, θ₂ = 50, and θ₃= 80, and the distance are d₁ = 5.00 m, d₂ = 8.00 m, and d₃ = 12.0 m. What are the (a) magnitude and (b) angle of the skunk’s displacement from i to f?

[PLAIN]http://sadpanda.us/images/355466-G1WEH29.jpg

Homework Equations

Using basic trigonometric functions, soh cah toa
Let X and Y stands for the summation of x and y.
Resultant vector = (X² + Y²)^1/2
Let * stands for the resultant vector angle, then * = tan^-1 = Y / X

The Attempt at a Solution

I have obtained the x and y component for d₁. Finding x = (5.00 m)cos30 = 4.33 m and for y, (5.00m)(sin30) = 2.5 m. However, I'm having the difficulty to find the other x and y components of d₂ and d₃ because they aren't parallel to x and y-axis respectively.

For example, d₂ is diagonal and I can't simply do (8.00 m)(cos 50) to find the x component because d₂ is not parallel to x axis. Hence, connecting d₁ and d₂ will not form a right triangle which is necessary to find the x and y components using soh cah toa..

Please give me an idea how to solve this..

Thank you..

PS. If the image link above doesn't work, pls. see the copy of this question in the attached file herein..

 

[anathema]

To solve this problem, you will need to use vector addition to find the overall displacement of the skunk from point i to point f. This involves breaking each displacement vector (d1, d2, and d3) into its x and y components, and then adding them together.

To find the x and y components of d2, you can use the law of cosines to find the angle between d1 and d2, and then use the law of sines to find the length of the component of d2 that is parallel to the x-axis. Similarly, you can use the law of cosines to find the angle between d2 and d3, and then use the law of sines to find the length of the component of d3 that is parallel to the y-axis.

Once you have all the x and y components, you can add them together to find the overall displacement. The magnitude of the displacement can be found using the Pythagorean theorem, and the angle can be found using the inverse tangent function.

Hope this helps! Good luck with your calculations.
Scientist