Components: A teacher sends her students on a treasure hunt. She gives the following instructions: 1. Walk 300 m north
2) Walk 400 m northwest
3) Walk 700 m east-southeast and the treasure is buried there.
As all the other students walk off following the instructions, Jane physics student quickly adds the displacements and walks in a straight line to find the treasure. How far and in what direction does Jane need to walk?

Question

Quizplus · Accepted Answer

We can break down the given directions into their corresponding northward and eastward components:
- Step 1: 300 m north = 0 m north + 300 m east (since there is no eastward component)
- Step 2: 400 m northwest = 283 m north + 283 m west (using Pythagoras' theorem, i.e. 400/sqrt(2) = 283)
- Step 3: 700 m east-southeast = 383 m south + 575 m east (using trigonometry, i.e. 700*cos(67.5) = 575 and 700*sin(67.5) = 383)

Now we can add up the northward and eastward components separately:
- Northward component: 0 m + 283 m - 383 m = -100 m
- Eastward component: 300 m + 283 m + 575 m = 1158 m

Therefore, the total displacement (i.e. the straight-line distance and direction) that Jane needs to walk is given by:
sqrt((-100)^2 + (1158)^2) = 481 m (using Pythagoras' theorem)
atan((-100)/(1158)) + 90 = 40.9° north of east (using trigonometry to find the angle relative to east and adding 90° to get the angle relative to north)

Components: a Teacher Sends Her Students on a Treasure Hunt