A teacher sends her students on a treasure hunt. She gives the following instruc

Question

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, Joe physics student quickly adds the displacements and walks in a straight line to find the treasure. How far and in what direction does Joe need to walk?

A) 399 m in a direction 52.5° north of east
B) 187 m in a direction 67.3° north of east
C) 284 m in a direction 28.2° west of north
D) 481 m in a direction 40.9° north of east
E) The treasure position cannot be reached in one straight walk.

I'm confused with this question..

Please provide full explanation ..

Explanation / Answer

Here ,

let east be the x -direction

north is the +ve y - direction

net displacement , dnet = d1 + d2 +d3

dnet = 300 j + 400 *(-cos(45) i + j*sin(45)) + 700 *(cos(22.5) i - j * sin(22.5))

solving for dnet

dnet = 363.9 i + 315 j N

|dnet| = sqrt(363.9^2 + 315^2)

|dnet| = 481.3 m

angle = arctan(315/363.9)

angle = 40.9 degree

the displacement for jog is 481 m in a direction 40.9° north of east

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