one day you go hiking at a nearby nature preser. At first, you follow the straig
ID: 2132233 • Letter: O
Question
one day you go hiking at a nearby nature preser. 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 degrees to follow a 2nd trail for 1.40 miles. Next, you turn to your right by 160 degrees and follow a 3rd trail for 2.20 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 through the woods(ignoring the trails). How far to the right should you turn, and how far do you have to walk, to go directly back to your starting point?
Turn blank degrees to the right and then walk blank miles
Explanation / Answer
net displacement in the eastern direction is
2 + 1.40 cos 30 + 2.20 cos (360 -160 + 30)
= 0.483 m toward east.
Net displacement in the northern direction is
1.4 sin 30 + 2.20 sin (360 -160 + 30)
= - 2.74
Minus indicates that he has moved to south
Resultant sqrt (0.483 ^2 + [- 2.74 ^2]) = 2.78
2.78 cos theta = 0.483
theta = 79.97 deg
2.78 sin theta = - 2.74
theta = - 9.59 deg
tan theta = - 2.74 / 0.483
theta = - 79.9 deg
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