One day you go hiking at a nearby nature preserve. At first, you follow the stra

Question

One day you go hiking at a nearby nature preserve. At first, you follow the straight, clearly marked trails. From your starting point, you travel 2.00 miles down the 1st trail. Then you turn to your left by 30.0 degree to follow a 2nd trail for 1.50 miles. Next, you turn to your right by 160% and follow a 3rd trail for 1.90 miles. At this point you are getting very tired and would like to get back as quickly as possible, but all of the available trails seem to lead you deeper into the woods. You would like to take a shortcut directly through the woods (ignoring the trails). How far to your right should you turn, and how far do you have to walk, to go directly back to your starting point? Feel free to use the provided vector drawing board to help visualize your work. Turn Number degree to the right then walk Number miles

Explanation / Answer

Taking the initial direction of the person as east,

Net displacement in the eastern direction is 2 + (1.5 cos 30°) + (1.9 cos (360 -160 + 30)) = 2.08 miles toward east.

Net displacement in the northern direction is (1.5 sin 30°) + (1.9 sin (360 -160 + 30)) = - 0.705 miles (Minus indicates that he has moved to south Resultant)

Resultant, D = (2.082 + (-0.705)2) = 2.20 miles

Theta = tan-1(-0.705/2.08) = -18.72° Or 341.28° from positive x-axis

Please rate my answer if you find it helpful m good luck...

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.