A car travels 15.5 km due north and then
38.6 km in a direction φ = 74.3
◦ west of
north.Find the magnitude of the car’s resultant
displacement.
Answer in units of km
d=15.5N+38.6cos74.3 N + 38.6Sin74.3 W
combine the N, then the W
mag d= sqrt (n^2 + W^2)
To find the magnitude of the car's resultant displacement, we can use the Pythagorean theorem.
Step 1: Convert the vector components to x and y coordinates.
The car travels 15.5 km due north, so its y-coordinate is 15.5 km.
The car travels 38.6 km in a direction of 74.3° west of north, so we need to find the x-coordinate using trigonometry.
x = 38.6 km * cos(74.3°)
Step 2: Calculate the magnitude of the resultant displacement using the Pythagorean theorem.
Magnitude = √(x^2 + y^2)
Let's plug in the values and solve the equation:
Magnitude = √((38.6 km * cos(74.3°))^2 + (15.5 km)^2)
Now we can calculate it:
Magnitude ≈ √((38.6 km * 0.2757)^2 + (15.5 km)^2)
Magnitude ≈ √((10.644 km)^2 + (15.5 km)^2)
Magnitude ≈ √(113.469 km^2 + 240.25 km^2)
Magnitude ≈ √(353.719 km^2)
Magnitude ≈ 18.80 km
Therefore, the magnitude of the car's resultant displacement is approximately 18.80 km.