While exploring a cave, a spelunker starts at the entrance and moves the following distances in horizontal plane. She goes 50.0 m West, 150 m North, 80 m 60 ° S of E.
a) Draw the figure applying polygon method. (scale 40 m: 1 cm)
b) Find her resultant displacement from the cave entrance applying component method
a) To draw the figure using the polygon method, we will first draw a scale. Since the scale is 40 m: 1 cm, we can represent 50.0 m as 1.25 cm, 150 m as 3.75 cm, and 80 m as 2.0 cm.
Start by drawing a line representing the 50.0 m distance towards the west from the entrance. Label this line as "50.0 m West."
Next, draw a line representing the 150 m distance towards the north from the end of the line representing the 50.0 m distance. Label this line as "150 m North."
Finally, draw a line representing the 80 m distance in the direction 60 ° south of east from the end of the line representing the 150 m distance. Label this line as "80 m 60 ° S of E."
Connect the starting point at the entrance to the endpoint of the line representing the 80 m distance to form a closed polygon.
b) To find the resultant displacement using the component method, we need to break down the distances into their horizontal (east-west) and vertical (north-south) components.
For the 50.0 m distance west, the horizontal component is -50.0 m (negative because it is towards the west), and the vertical component is 0 m.
For the 150 m distance north, the horizontal component is 0 m, and the vertical component is +150 m (positive because it is towards the north).
For the 80 m distance 60 ° south of east, we need to determine the horizontal and vertical components.
The horizontal component can be found by calculating the cosine of 60° and multiplying it by the distance of 80 m. Therefore, the horizontal component is 80 m * cos(60°) = 40 m.
The vertical component can be found by calculating the sine of 60° and multiplying it by the distance of 80 m. Therefore, the vertical component is 80 m * sin(60°) = 69.3 m.
Now, we can add up the horizontal and vertical components to find the resultant displacement.
Horizontal component: -50.0 m + 40 m = -10.0 m (negative because it is towards the west)
Vertical component: 0 m + 150 m + 69.3 m = 219.3 m
The resultant displacement from the cave entrance is -10.0 m west and 219.3 m north.