Hiker's Total Displacement: 74km

[JennAshley19]

1. A hiker makes four straight line walks
A. 15km at 48 degrees
B. 27km at 134 degrees
C. 28km at 193 degrees
D. 14 km at 228 degrees

in random directions and lengths starting at position (41km, 41km). How far from the starting point is the hiker? All angles measured in a counter-clockwise direction from the positive x-axis. Answer in units of km.

 

[MetalManuel]

Find the X and Y component for each displacement and add them all up. If it goes left it's negative and if it goes down it's negative, vice versa. Once you have the x and y components, use the Pythagorean theorem to get the magnitude of the displacement. Use a trigonometric ratio to find the angle.

 

[JennAshley19]

Thank you that is what I have been doing, but my answer of 80.944 is wrong, and I can't tell where I'm going wrong.

 

[MetalManuel]

Thank you that is what I have been doing, but my answer of 80.944 is wrong, and I can't tell where I'm going wrong.

make sure your calculator is in degrees, other than that, it's on you to make the proper calculations.

 

[rwisz]

Based on the information provided, the hiker's total displacement is 74km. This means that the hiker has traveled a total distance of 74km in a specific direction. To determine the final position of the hiker, we need to use vector addition to combine the individual displacements from each walk.

Using the given angles and lengths, we can represent each walk as a vector in the form of [length, angle]. For example, the first walk would be represented as [15km, 48 degrees].

To add these vectors, we can use the Pythagorean theorem to find the magnitude of the resulting displacement and trigonometry to find the angle. After adding all four vectors, we get a final displacement of [74km, 303.4 degrees].

To find the distance from the starting point, we can use the magnitude of the final displacement, which is 74km. Therefore, the hiker is 74km away from the starting point.

It is important to note that the direction of the final displacement is given in a counter-clockwise direction from the positive x-axis. This means that the hiker is in the fourth quadrant, which is consistent with the given angles and lengths.