A car travels 30km due south and then 40km west, what is its resultant from the starting point?
This is a Pythagorean theorem problem.
Think of a triangle that is pointing up. The side that goes down to the 90 degree angle is 30km long, and the side going left from there is 40 km long. You need to determine the hypotenuse of the triangle.
a^2+b^2=c^2
30^2+40^2=c^2
2500=c^2
sqrt(2500=c
c=50 km
To find the resultant displacement from the starting point, we can use the Pythagorean theorem, as the car's motion forms a right triangle.
1. Draw a diagram to visualize the problem. In this case, a right triangle can be formed with the car's movements southeast and west.
(Start)
|
| 30 km
|
↓
←40 km | ← Resultant
|
↓
2. Use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.
Let's represent the distance traveled south as one leg (side A), the distance traveled west as another leg (side B), and the resultant displacement as the hypotenuse (side C).
So, A = 30 km and B = 40 km.
Applying the Pythagorean theorem: C² = A² + B²
substituting the values: C² = (30 km)² + (40 km)²
3. Calculate the squares: C² = 900 km² + 1600 km²
4. Add the squares together: C² = 2500 km²
5. Take the square root of both sides to find the value of C: C = √2500 km²
6. Calculate the square root: C = 50 km
Therefore, the resultant displacement from the starting point is 50 km.