A man walks 5 m at 37 degree north of east then 10 m at 60 degree west of north.?
calculate the magnitude and direction of his displacement.
See previous post: Sat, 1-3-15, 4:01 AM.
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To calculate the magnitude and direction of displacement, we can break down the given motion into two components: east-west (x-direction) and north-south (y-direction).
First, let's calculate the east-west component of the displacement:
- The man walks 5 m east at an angle of 37 degrees north of east.
- This means that the east-west component of displacement is given by: (5 m) * cos(37°).
Next, let's calculate the north-south component of the displacement:
- The man then walks 10 m north at an angle of 60 degrees west of north.
- This means that the north-south component of displacement is given by: (10 m) * sin(60°).
Now, we can calculate the magnitude of displacement using the Pythagorean theorem:
- The magnitude of displacement (d) is given by: √[(east-west component)^2 + (north-south component)^2].
Lastly, we can calculate the direction of displacement using the inverse tangent (arctan) function:
- The direction (θ) of displacement is given by: arctan(north-south component / east-west component).
Let's substitute the values into the formulas:
First, calculate the east-west component of displacement:
East-west component = (5 m) * cos(37°) = 5 m * 0.7986 ≈ 3.993 m (rounded to three decimal places).
Next, calculate the north-south component of displacement:
North-south component = (10 m) * sin(60°) = 10 m * 0.8660 ≈ 8.660 m (rounded to three decimal places).
Now, calculate the magnitude of displacement:
Magnitude of displacement (d) = √[(3.993 m)^2 + (8.660 m)^2] ≈ √(15.944049 + 75.00676) ≈ √90.950809 ≈ 9.538 m (rounded to three decimal places).
Finally, calculate the direction of displacement:
Direction (θ) = arctan(8.660 m / 3.993 m) ≈ arctan(2.166750963) ≈ 65.476° (rounded to three decimal places).
Therefore, the magnitude of the man's displacement is approximately 9.538 meters, and the direction is 65.476 degrees.