question archive A teacher sends her students on a treasure hunt
A teacher sends her students on a treasure hunt
Subject:PhysicsPrice:2.87 Bought7
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.
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Answer:
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
