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8 February, 04:31

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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Answers (1)
  1. 8 February, 06:55
    0
    D) Joe need to walk 481 m in a direction 40.9° north of east

    Explanation:

    Given:

    1. Walk 300 m north

    2. Walk 400 m northwest

    3. Walk 700 m east-southeast and the treasure is buried there

    Taking north as positive y axis and east as positive x axis.

    Resolving their positions into x and y vector components.

    1. d1 = 300j

    2. d2 = - 400cos45i + 400sin45j

    3 d3 = 700cos22.5i - 700sin22.5j

    Resultant position.

    d = d1+d2+d3

    d = (-400cos45 + 700cos22.5) i + (300+400sin45-700sin22.5) j

    d = (363.873) i + (314.964) j

    D = √ ((363.873) ^2 + (314.964) ^2)

    D = 481.25m ~ = 481m

    Angle = taninverse (314.964/363.873)

    Angle = 40.9°

    Since the x and y components are both positive, it implies that their position is north of east

    Therefore, Joe need to walk 481 m in a direction 40.9° north of east
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