uestion 3 of 10 Sapling Learning nature first, you follow the straight, clearly

Question

uestion 3 of 10 Sapling Learning nature first, you follow the straight, clearly marked trails. From your 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. and follow a 3rd trail for 1.80 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 directly through the woods (ignoring the a shortcut 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. Number o to the right, Turn Number then walk miles 0.25 miles Note: The vector drawing board is meant as a uide and a reality check, but may not give you e answers with sufficient precision. It is preferable to calculate the magnitude and direction by hand. O Previous Check Answer 0 Next d Exit

Explanation / Answer

Here ,

for the net displacement

let the initial direction is x direction and the direction to the right 90 degree is y direction

Now,

Dnet = 2 i + 1 * (cos(30) i - j * sin(30)) + 1.80 * (cos(130 degree) i + j * sin(130 degree))

Dnet = (2 + cos(30) + 1.80 * cos(130 degree) ) i + j * (- sin(30) + 1.80 * sin(130)) miles

Dnet = 1.71 i + 0.88 j miles

Dnet = sqrt(1.71^2 + 0.88^2) at arctan(0.88/1.71) degree

Dnet = 1.92 miles at 27.23 degree

turning angle = (180 - 130) + 27.2 degree = 77.2 degree right

he shall turn right by 77.2 degree

distance he shall walk is 1.92 miles

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