A boy moves 4 m south and 5 m in direction 37•N O E.find resultant displacement?

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Calculation of Resultant Displacement

Start by drawing a diagram of the boy's movements. Draw an arrow pointing south to represent the 4 m southward movement, and another arrow pointing in the direction 37° N O E to represent the 5 m movement in that direction.

Using the pythagorean theorem, calculate the magnitude of the resultant displacement by squaring each of the individual vectors, adding them together, and taking the square root of the sum.
- Square of the southward movement: 4^2 = 16
- Square of the 37° N O E movement: 5^2 = 25
- Sum of squares: 16 + 25 = 41
- Square root of sum: sqrt(41) = 6.4

Determine the direction of the resultant displacement using trigonometry.
- First, find the angle that the resultant vector makes with the southward vector. This angle can be found using the inverse tangent function: tan^-1(5/4) = 51.3°.
- Next, add this angle to the angle of the southward vector (180°) to find the angle that the resultant vector makes with due north: 51.3° + 180° = 231.3°.
- Finally, subtract this angle from 360° to find the angle that the resultant vector makes with due east: 360° - 231.3° = 128.7°.

The direction of the resultant displacement is 6.4 m at an angle of 128.7° east of due north.

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