A person walks 25 m west and then 45 m at an angle of 60 degrees north of east. What is the magnitude of the total displacement?

To solve this question, we need to use the component method and split our displacements into their x and y vectors. We will assign north and east as the positive directions.
The first movement of 25m west is already split. x = -25m, y = 0m.
The second movement of 45m [E60N] needs to be split using trig. x = 45cos60 = 22.5m y = 45sin60 = 39.0m
Then, we add the two x and two y displacements to get the total displacement in each direction.
x = -25m + 22.5m = -2.5m y = 0m + 39.0m
We can use Pythagorean theorem to find the total displacement. d² = x² + y² d = √(-2.5² + 39²) d = 39.08m
And then we can use tan to find the angle. inversetan(y/x) = angle inversetan(39/2.5) = 86.3
Therefore, the total displacement is 39.08m [W86.3N]

Answered by chipperrider | 2024-06-24

The total displacement after walking 25 m west and then 45 m at an angle of 60 degrees north of east is approximately 39.1 m at an angle of about 86.3° north of west. This was calculated by determining the x and y components of each leg of the journey, summing them, and applying the Pythagorean theorem. The resulting displacement indicates how far the person is from the starting point and in which direction.
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Answered by chipperrider | 2024-09-05