Mapat Sapling Learning One day you go hiking at a nearby nature preserve. At fir
ID: 1771027 • Letter: M
Question
Mapat Sapling Learning One day you go hiking at a nearby nature preserve. At first, you follow the straight, clearly marked trails. From r starting point, you travel 2.00 miles down the 1st trail. Then you tum to your left by 30.0 to follow a 2nd trail for 1.20 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 trails). How far to your right should you turn, and how far do you have to walk, to go starting point? h the woods (ignoring the y back to your Feel free to use the provided vector drawing board to help visualize your work. Number 0.25 miles Note: The vector drawing board is meant as a uide and a reality check, but may not give you Turn to the right, e answers with sufficient precision. It is preferable to calculate the magnitude and direction by hand. Number then walk milesExplanation / Answer
Total displacement = [ 2+1.20*cos 30 degree + 1.90* cos (30 degree - 160 degree )] j
+ [ -1.20*sin 30 degree - 1.90* sin (30 degree - 160 degree )] i
= 1.8179j + 0.8555i
= sqrt(1.8179^2 + 0.8555^2) = 2.009 miles
angle = 180+30-160 + arctan(0.8555/1.8179) = 75.2 degree
Turn angle = 75.2 degree answer