Question

You walk 4.5 km in one direction and then turn 45 degrees to the right and walk another 6.4 km. What is the magnitude of displacement?

a) 9.6 km
b) 10.3 km
c) 11.2 km
d) 12.5 km

Answer 1

The magnitude of displacement is 5.52 km.

Step-by-step explanation:

To find the magnitude of displacement, we need to use the Pythagorean Theorem.

First, we can break down the displacement into its horizontal and vertical components.

The horizontal component is 4.5 km * cos(45°) = 3.182 km

The vertical component is 6.4 km * sin(45°) = 4.527 km

Now, we can use the Pythagorean Theorem to find the displacement:

Displacement = √(3.182 km)^2 + (4.527 km)^2 = √(10.117 km^2 + 20.5 km^2) = √(30.617 km^2) = 5.52 km

Therefore, the magnitude of displacement is 5.52 km.