A car travels 3 km due north, then 5 km east. represent these displacement graphically and determinethe resultant displacement.
√(3^2+5^2) = ____
To represent the displacement graphically, we can use a coordinate system with the origin as the starting point of the car. Since the car travels 3 km north first, we move up 3 units on the y-axis from the origin. Then, it travels 5 km east, so we move 5 units to the right on the x-axis. The final position is where the car ends up, denoted by a point.
Here is the graphical representation of the car's displacement:
```
|
|
| x
-------O-------
```
The point (5, 3) represents the car's final position in the coordinate system.
To find the resultant displacement, we can use the Pythagorean theorem. The horizontal displacement (5 km east) and the vertical displacement (3 km north) form a right-angled triangle. The resultant displacement (R) is the hypotenuse of this triangle.
Using the Pythagorean theorem, we can calculate R:
R = √(5^2 + 3^2)
= √(25 + 9)
= √34 km
Therefore, the resultant displacement is approximately 5.83 km at a 57.99° angle above the horizontal axis.