Free. Exclusive. Just for you.
Four unique services that make learning easier, faster, and smarter - only on our website.

Treasure map with a blue path leading to a chest, marked with a red arrow and ruler, on a grid with a scale of 1 box side = 1.0 m.

Map to Leadbelly's Treasure showing a grid path with a pirate character, compass, treasure chest, and scale indicating 1 box side = 1.0 m.

Map to Leadbelly's Treasure showing a grid path with a pirate character, compass, treasure chest, and scale indicating 1 box side = 1.0 m.

JPG 817×615 96.3 KB Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #662338
Show Answer Key & Explanations Step-by-step solution for: Distance vs Displacement — Team of Teachers
Let's solve the problem step by step using the map titled "Map to Leadbelly's Treasure".

---

🔍 Understanding the Map



We are given:

- A grid map with a scale: 1 box side = 1.0 meter
- A starting point marked with a blue "X" near the pirate character.
- A treasure chest marked with a red "X".
- A blue path showing the route taken (possibly a detour or clue).
- A compass rose indicating directions (N, E, S, W).
- Tools shown: a ruler and a protractor — suggesting we may need to measure distance and direction.

Our goal is likely to determine the direct displacement from the starting point (blue X) to the treasure (red X) in terms of:
- Distance (in meters)
- Direction (angle from North or another reference)

---

🧭 Step 1: Identify Coordinates



We'll assign coordinates to the starting point and the treasure.

Assume the bottom-left corner of the grid is (0, 0), and each square is 1 meter.

#### Starting Point (Blue X):
- Located at approximately (3, 5) → let’s count carefully:
- From the left edge: 3 boxes right
- From the bottom: 5 boxes up

So, Start = (3, 5)

#### Treasure (Red X):
- Located at approximately (12, 9)
- 12 boxes right from the left
- 9 boxes up from the bottom

So, Treasure = (12, 9)

---

📏 Step 2: Calculate Displacement



We now calculate the horizontal (east-west) and vertical (north-south) components of the displacement.

- Δx (East-West):
$ 12 - 3 = 9 $ meters east

- Δy (North-South):
$ 9 - 5 = 4 $ meters north

So, the displacement vector is 9 m east and 4 m north.

---

📐 Step 3: Find the Straight-Line Distance



Use the Pythagorean Theorem:

$$
\text{Distance} = \sqrt{(Δx)^2 + (Δy)^2} = \sqrt{9^2 + 4^2} = \sqrt{81 + 16} = \sqrt{97} \approx 9.85 \text{ meters}
$$

Distance ≈ 9.85 meters

---

🧭 Step 4: Find the Direction (Bearing)



We want the angle θ measured from North, clockwise (standard bearing).

But since we have:
- East component: 9 m
- North component: 4 m

This forms a right triangle where:
- Opposite = 9 m (East)
- Adjacent = 4 m (North)

So,

$$
\tan(\theta) = \frac{9}{4} = 2.25
\Rightarrow \theta = \tan^{-1}(2.25) \approx 66.0^\circ
$$

This means the direction is 66 degrees east of north, or a bearing of 66°.

Direction: 66° from North toward East

---

Final Answer:



To reach Leadbelly's treasure directly from the starting point:

- Distance: Approximately 9.85 meters
- Direction: 66° east of north (or bearing 66°)

---

🧩 Optional: What About the Blue Path?



The blue arrows show a winding path that might represent a riddle or challenge, but since the red line goes straight from start to treasure, it appears the direct path is what we're being asked to find.

Also, the ruler and protractor suggest measuring this direct vector.

---

🎯 Conclusion



> The treasure is located 9.85 meters away at a bearing of 66° from the starting point.

You can walk 9.85 meters in a direction 66° east of north to reach the treasure directly.

---

Let me know if you'd like a visual sketch or how to use the ruler/protractor on the image!
Parent Tip: Review the logic above to help your child master the concept of distance and displacement practice worksheet.
Print Download

How to use

Click Print to open a print-ready version directly in your browser, or use Download to save the file to your device. The ⭐ Answer button generates an AI answer key instantly - useful for teachers who need a quick reference. Need a different version? Our AI Worksheet Generator lets you create a custom worksheet on any topic in seconds.

(view all distance and displacement practice worksheet)

SOLUTION: Distancr and displacement practice - Studypool
Distance & Displacement worksheet | Live Worksheets
Ch 2 Motion practice problems
Distance, Displacement, Speed, and Velocity - Worksheet ...
Motion, distance, displacement, speed, velocity and acceleration.
Distance vs Displacement — Team of Teachers
Lesson 2.1 - Distance & Displacement - Classful
Distance And Displacement Worksheet Answer Key Pdf - Fill Online ...
Distance and Displacement Worksheet 1 | PDF
Distance-and-Displacement-Practice-Worksheet3.pdf | Slides Physics ...