Displacement

Question

A particle moves 30 m north, then 40 m east, and finally 50 m south. What is the magnitude of its displacement (approximately)?

RankGuru · Accepted Answer

1. **Vector Components**: Let East be $+X$ ($\hat{i}$) and North be $+Y$ ($\hat{j}$).
   - $\vec{s}_1 = 30 \hat{j}$ (North).
   - $\vec{s}_2 = 40 \hat{i}$ (East).
   - $\vec{s}_3 = -50 \hat{j}$ (South).
2. **Summing Vectors**:
   - $\vec{s}_{net} = 40 \hat{i} + (30 - 50) \hat{j} = 40 \hat{i} - 20 \hat{j}$.
3. **Calculate Magnitude**:
   - $|s| = \sqrt{40^2 + (-20)^2} = \sqrt{1600 + 400} = \sqrt{2000}$.
4. **Final Value**:
   - $|s| = 20\sqrt{5} \approx 20 	imes 2.236 \approx 44.72$ m.
5. **Approximate Answer**: **45 m**.

Rank Guru

Displacement

Select the correct option:

Solution

🔒 Solution Hidden from View

More displacement Practice Questions

With the same data (α = 4 rad/s²), angular displacement in first 5 s?

Maximum speed occurs at what displacement in SHM?

A runner completes one full lap of a 400 m circular track in 60 s. Which statement is correct about ...

Velocity of a particle varies as v = 4t (m/s). Find displacement in first 5 s (starts at origin).

A boat travels 12 km east, then 5 km north. What is the magnitude of net displacement?

A wheel rotates with a constant angular velocity of 4 rad/s. How many complete revolutions does it m...

About This Question