A boy walked 100km due east then walks 120km due north and 110km at 45°northeast.What's his resultant displacement?
To find the resultant displacement of the boy, we need to combine the individual displacements in both magnitude and direction.
1. Start by drawing a rough sketch of the given information. Place a coordinate system with the starting point of the boy as the origin (0,0).
2. The boy's first displacement is 100km due east, which means we move 100km in the positive x-direction. Mark this point on the sketch.
3. Next, the boy walks 120km due north, which means we move 120km in the positive y-direction. From the end point of the previous step, draw a vertical line 120km long.
4. The boy's last displacement is 110km at 45° northeast. To determine the horizontal and vertical components of this displacement, we need to use trigonometry. The horizontal component can be found by multiplying the magnitude (110km) by the cosine of the angle (45°). The vertical component can be found by multiplying the magnitude (110km) by the sine of the angle (45°).
Horizontal component = 110km * cos(45°)
Vertical component = 110km * sin(45°)
5. Measure the horizontal component from the previous point towards the east and the vertical component upwards. Mark the end point using these components.
6. Finally, draw a straight line from the starting point to the end point, which represents the resultant displacement.
7. Measure the magnitude (length) of the resultant displacement using a ruler or a measuring tool. Similarly, measure the angle that the resultant displacement makes with the positive x-axis using a protractor.
These measurements will give you the magnitude and direction of the boy's resultant displacement.