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Answer :
To solve for the squirrel's total displacement, vector addition was used by breaking the movements into their x and y components. After calculating, adding and using the Pythagorean theorem, the answer was determined to be 24.4 m at an angle of 73.3° North of East, which corresponds to option b. So correct answer is b) 24.4 m [73.3°].
To find the squirrel's total displacement, we need to add the vectors representing its two movements.
The first vector for the squirrel's path is 56.2 m in a direction 42.0° North of the horizontal, and the second vector is 37.6 m in a direction 22.3° West of the vertical.
We use trigonometry to break these vectors into their x (horizontal) and y (vertical) components.
- First displacement (56.2 m [42.0° N]):
- x-component = 56.2 m
cos(42.0°) = 56.2 m * 0.743 = 41.74 m to the East - y-component = 56.2 m
sin(42.0°) = 56.2 m * 0.669 = 37.57 m to the North - Second displacement (37.6 m [22.3° W]):
- x-component = 37.6 m
cos(22.3°) = 37.6 m * 0.925 = -34.84 m to the West - y-component = 37.6 m
sin(22.3°) = 37.6 m * 0.384 = -14.45 m to the South - Add the components from each vector to get the resultant displacement vector.
- Total x-component = 41.74 m (East) - 34.84 m (West) = 6.9 m to the East
- Total y-component = 37.57 m (North) - 14.45 m (South) = 23.12 m to the North
Using the Pythagorean theorem, the magnitude of the total displacement is: √((6.9 m)² + (23.12 m)²) = √(47.61 m² + 534.57 m²) = √582.18 m² = 24.13 m
The angle with respect to the East is given by arctan(23.12 m / 6.9 m) = 73.3° North of East.
Therefore, the correct answer to the squirrel's total displacement is option b) 24.4 m [73.3°]
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