Question

A car is driven east for a distance of 46 km, then north for 19 km, then in a direction 30 degrees east of north for 25 km. Determine the magnitude of the displacement (in kilometers) of the car from its starting point.

Answer 1

The car's displacement can be found by using vector addition and the Pythagorean theorem.

First, let's break the final displacement into north and east components. The northward component is 25 km * cos(30°), and the eastward component is 25 km * sin(30°).

Adding up all of the displacement components:

Northward: 19 km + 25 km * cos(30°) ≈ 40.5 km

Eastward: 46 km + 25 km * sin(30°) ≈ 58.5 km

Then, use the Pythagorean theorem to find the magnitude of the total displacement:

√[(40.5 km)^2 + (58.5 km)^2] ≈ 70.4 km

So the car's displacement from the starting point is approximately 70.4 km.