Due Date Points Po Grade Ca Descriptic Policies: Sapling Learning Mapob One day

Question

Due Date Points Po Grade Ca Descriptic Policies: Sapling Learning Mapob One day you go hiking at a nearby nature preserve. At first, you follow the straight, clearly marked trails. From you r starting point, you travel 2.00 miles down the 1st I. Then you turn to your left by 30.0° to follow a 2nd and follow a 3rd trail for 2.00 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 You can c d1 You can up on an far do you have to walk, to go directly back to your starting point? You can you get i Feel free to use the provided vector drawing board to help visualize your work. You lose in your q answer 0.25 miles Number Note: The vector drawing board is meant as a guide and a reality check, but may not give you the answers with sufficient precision. It is preferable to calculate the magnitude and direction by hand. O eTexth O Help V Web OTechn Turn 86.12 to the right, Turn!! 86.12 | o | to the right, Number then walk 2.29 miles

Explanation / Answer

As you have already turned left 30 degrees from your original path, turning right 160 degrees means your line of travel is 160 - 30 = 130 degrees from your original path.

at turn about point your distance traveled parallel to your original path is

d1 = 2.00 + 1.60 cos30 + 2.00cos(-130)

d1 = 2.1 miles

the distance traveled perpendicular to the original path is

d2 = 0 + 1.60sin30 + 2.00sin(-130)

d2 = -0.73 miles

so your distance back to the starting point is

d = (2.1)² + (-0.73)²)

d = 2.22 miles (ans)

If we assume the original direction was zero degrees with positive angles in the counter clockwise direction, your first turn had you heading +30°. Your second heading had you heading -130° which is the same as 360 - 130 = 230°.

Your new heading needs to be

tan = dy/dx

tan = -0.73 / 2.1

= 160.83°

[Arc-tangent of negative numbers have 2 possible results. Calculators always put results in the 4th quadrant. However, tangent is the change in y over the change in x. As the change in x was a negative value and y was positive, that makes the answer in the 2nd not the 4th quad.

-19.168 + 180 = 160.83]

which means we need to turn right

230° - 160.83° = 69.2° (ans)

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