What is the total displacement of two trips one 10km north and the other 24km east
To find the total displacement of two trips, one going 10km north and the other 24km east, we can use the Pythagorean theorem.
1. First, we need to calculate the horizontal and vertical displacements separately.
- The horizontal displacement is the distance traveled east, which is 24km.
- The vertical displacement is the distance traveled north, which is 10km.
2. Next, we can use the Pythagorean theorem (a^2 + b^2 = c^2) to find the total displacement.
a = horizontal displacement = 24km
b = vertical displacement = 10km
c = total displacement (hypotenuse)
Plugging in the values, we have:
(24km)^2 + (10km)^2 = c^2
576km^2 + 100km^2 = c^2
676km^2 = c^2
3. To find c, we need to take the square root of both sides of the equation.
√(676km^2) = c
c ≈ 26km
Therefore, the total displacement of the two trips, one going 10km north and the other 24km east, is approximately 26km.
To find the total displacement of two trips, you need to combine their individual displacements using vector addition.
First, let's represent the displacement of the first trip, which is 10 km north, as a vector. We can call this vector "A," and its direction will be north. The magnitude of this vector will be 10 km.
Next, let's represent the displacement of the second trip, which is 24 km east, as another vector. We can call this vector "B," and its direction will be east. The magnitude of this vector will be 24 km.
To add these two vectors together, we can use the Pythagorean theorem because the vectors are perpendicular to each other. The Pythagorean theorem states that the sum of the squares of the lengths of the perpendicular sides of a right triangle is equal to the square of the length of the hypotenuse.
So, we can calculate the magnitude of the total displacement vector, which we can call "C," using the following formula:
C^2 = A^2 + B^2
Plugging in the values, we get:
C^2 = (10 km)^2 + (24 km)^2 = 100 km^2 + 576 km^2 = 676 km^2
To find the total displacement, we take the square root of both sides of the equation:
C = √676 km^2 = 26 km
Therefore, the total displacement of the two trips combined is 26 km.
x^2 = (10)^2 + (24)^2
Solve for x.