An RV travels 45 km east and stays the night at a KOA. The next day it travels for 3 hours to the north, traveling 110 km. What is the displacement over the two days for the RV?
Please help, thank you!
what is sqrt(110^2+45^2)
at an angle of arctan45/110 E of N
what is sqrt(110^2+45^2)
118.849
at an angle of arctan45/110 E of N
^^^ what's that for?
To find the displacement over the two days, we need to calculate the total change in position from the starting point to the ending point.
First, let's break down the RV's movements into horizontal (east/west) and vertical (north/south) components.
On the first day, the RV travels 45 km east. This defines the horizontal component of its displacement.
On the second day, it travels 110 km to the north. This defines the vertical component of its displacement.
Since these movements are at right angles to each other, we can use the Pythagorean theorem to find the total displacement. The theorem states that the square of the hypotenuse (displacement) is equal to the sum of the squares of the other two sides (horizontal and vertical components).
Using the theorem, we can calculate the total displacement as follows:
Displacement = √(horizontal component^2 + vertical component^2)
Horizontal component = 45 km (east)
Vertical component = 110 km (north)
Now we can calculate the total displacement:
Displacement = √((45 km)^2 + (110 km)^2)
Displacement = √(2025 km^2 + 12100 km^2)
Displacement = √(14125 km^2)
Displacement ≈ 118.8 km
Therefore, the RV's displacement over the two days is approximately 118.8 km.
To calculate the displacement of the RV, we need to determine the net distance and direction from the starting point to the ending point. In this case, the RV traveled 45 km east and then 110 km north.
To find the displacement, we can imagine drawing a straight line from the starting point to the ending point. The length of that line represents the displacement, and its direction can be determined by the angle it makes with the reference direction, typically north.
Now, since the RV first traveled 45 km east, we can consider that as the x-component of its displacement vector. Similarly, the subsequent 110 km north can be considered as the y-component of the displacement vector.
Using the Pythagorean theorem, we can calculate the displacement:
Displacement = √(x^2 + y^2)
Where x represents the eastward distance, and y represents the northward distance.
In this case, x = 45 km (east) and y = 110 km (north).
Substituting the values into the formula:
Displacement = √(45^2 + 110^2)
Displacement = √(2025 + 12100)
Displacement = √14125
Displacement ≈ 118.86 km
Therefore, the displacement over the two days for the RV is approximately 118.86 km.