A car travels 12 km due north and then 26.2 in a direction 0/( that is supposed to be a circle with a line through it)67.3 west of north. Find the magnitude of the cars resultant displacement
To find the magnitude of the car's resultant displacement, we can use the concept of vector addition.
First, we need to find the individual components of the car's displacement. We can break down the given distances into their respective north and west components.
The car travels 12 km due north, so its north component is 12 km.
The car then travels 26.2 km in a direction of 67.3° west of north. To find the west component, we need to calculate the projection of the displacement onto the west direction.
The west component = displacement * cos(angle)
= 26.2 km * cos(67.3°)
Calculating the west component by substituting the values:
west component = 26.2 km * cos(67.3°)
≈ 26.2 km * 0.389 (rounded to three decimal places)
≈ 10.167 km (rounded to three decimal places)
Now that we have the north and west components, we can use the Pythagorean theorem to find the magnitude of the car's resultant displacement.
Resultant displacement = √((north component)^2 + (west component)^2)
= √((12 km)^2 + (10.167 km)^2)
Calculating the resultant displacement:
resultant displacement ≈ √(144 km^2 + 103.376889 km^2)
≈ √247.376889 km^2
≈ 15.735 km (rounded to three decimal places)
Therefore, the magnitude of the car's resultant displacement is approximately 15.735 km.