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 ° to follow a 2nd trail for 1.40 miles. Next, you turn to your right by 160 ° and follow a 3rd trail for 1.70 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?

need to turn how many degrees to the right?

then walk how many miles?

Explanation / Answer

Considering north and east as positive,
And taking the initial direction of the person as east,

net displacement in the eastern direction is

2 + 1.4 cos 30 + 1.7 cos (360 -160 + 30) = 2.12 m toward east.

Net displacement in the northern direction is
1.4 sin 30 + 1.7 sin (360 -160 + 30) = - 0.6023
Minus indicates that he has moved to south

Resultant √ (2.12 ^2 + [- 0.6023 ^2]) = 2.204
2.204 cos θ = 2.12
θ = 15.9 ° south of east (below x axis)
2.204 sin θ = - 0.6023
θ = - 15.9 °
tan θ = - 0.6023/2.12
θ = - 15.9 ° or 344.1 ° from the positive x axis

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

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