Question

A displacement of magnitude \(32 \mathrm{cm}\) toward the east is followed by displacements of magnitude \(48 \mathrm{cm}\) to the east and then $64 \mathrm{cm}$ to the west. What is the total displacement?

Short answer

Answer: The total displacement is 16cm toward the East.

Step-by-step solution

Identify the given displacements and their directions

We are given three displacements in the problem: 1. A displacement of \(32cm\) to the east 2. A displacement of \(48cm\) to the east 3. A displacement of \(64cm\) to the west

Simplify the problem by combining same-direction displacements

The first two displacements are in the same direction (east), so we can add their magnitudes together: \(\displaystyle 32cm + 48cm = 80cm\) to the east. Now, our problem is simplified to finding the total displacement after two displacements: 1. A displacement of \(80cm\) to the east 2. A displacement of \(64cm\) to the west

Calculate the net displacement

Now, we calculate the net displacement by subtracting the displacements in opposite directions: \(\displaystyle 80cm - 64cm = 16cm\). Since the eastward displacement (80 cm) is greater than the westward displacement (64 cm), the total displacement is toward the east.

Write the final answer

The total displacement is \(16cm\) toward the east.