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Calculation of Resultant Displacement
To find the resultant displacement, we need to use vector addition. We are given two vectors, one moving 4 m south and the other moving 5 m in the direction of 37° north of east.
Vector Addition
To add vectors, we need to break them down into their x and y components. We can do this using trigonometry.
For the first vector moving 4 m south, the y component is -4 m (since south is in the negative y direction) and the x component is 0 m (since there is no movement in the x direction).
For the second vector moving 5 m in the direction of 37° north of east, we can find the x and y components using trigonometry. The angle between the vector and the x-axis is 37°, so the x component is 5 cos 37° = 3.98 m (rounded to two decimal places). The y component is 5 sin 37° = 3.00 m (rounded to two decimal places).
Now we can add the x and y components of the two vectors to find the resultant displacement.
Resultant Displacement
To find the resultant displacement, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the other two sides.
In this case, the x component is 3.98 m and the y component is -1.00 m (since the first vector moved 4 m south). Therefore, the hypotenuse (or resultant displacement) is:
sqrt((3.98)^2 + (-4)^2) = 5.14 m (rounded to two decimal places)
Therefore, the resultant displacement is 5.14 m.
To find the resultant displacement, we need to use vector addition. We are given two vectors, one moving 4 m south and the other moving 5 m in the direction of 37° north of east.
Vector Addition
To add vectors, we need to break them down into their x and y components. We can do this using trigonometry.
For the first vector moving 4 m south, the y component is -4 m (since south is in the negative y direction) and the x component is 0 m (since there is no movement in the x direction).
For the second vector moving 5 m in the direction of 37° north of east, we can find the x and y components using trigonometry. The angle between the vector and the x-axis is 37°, so the x component is 5 cos 37° = 3.98 m (rounded to two decimal places). The y component is 5 sin 37° = 3.00 m (rounded to two decimal places).
Now we can add the x and y components of the two vectors to find the resultant displacement.
Resultant Displacement
To find the resultant displacement, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the other two sides.
In this case, the x component is 3.98 m and the y component is -1.00 m (since the first vector moved 4 m south). Therefore, the hypotenuse (or resultant displacement) is:
sqrt((3.98)^2 + (-4)^2) = 5.14 m (rounded to two decimal places)
Therefore, the resultant displacement is 5.14 m.
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