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Distance Logic - Beginner-Intermediate Level: net displacement BEGINNER-INTERMEDIATE

This deep dive ★ worksheet contains 20 beginner-intermediate-level distance logic problems. Worksheet 11 of 30 focuses on net displacement. Practice route mapping, distance measurement, relative distances with our step-by-step solutions. Difficulty: building on fundamentals with moderate challenges. Recommended for developing learners.

📝 Worksheet 11 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 11 of 30 (36% complete)

Question 1

Two persons A and B start from the same point. A walks 17 m South, then 20 m South. B walks 6 m North, then 5 m West. What is the distance between them?
Step-by-step:
1. A's final position: (0, -37)
2. B's final position: (-5, 6)
3. Distance = √[(0--5)² + (-37-6)²] = √[5² + -43²] = 43 m
two-persons, relative, distance

Question 2

A runner runs at 6 m/s on a circular track of length 707 m for 153 seconds. How many laps does he complete?
Step-by-step:
1. Distance covered in 153 seconds = 6 × 153 = 918 m
2. Number of laps = Distance / Track length = 918 / 707 = 1.3 laps
circular, track, meeting, laps

Question 3

A boat travels at 12 km/h in still water. Stream speed is 5 km/h. What is the difference between upstream and downstream time for 68 km?
Step-by-step:
1. Downstream speed = 17 km/h, Time = 4.0 hours
2. Upstream speed = 7 km/h, Time = 9.7 hours
3. Difference = 9.7 - 4.0 = 5.7 hours
boat, stream, upstream, downstream

Question 4

A person travels 7 m West, then 24 m South. Find the shortest distance from the starting point.
Step-by-step:
1. West and South are perpendicular directions
2. Shortest distance = √(7² + 24²) = √625 = 25 m
shortest-path, pythagoras

Question 5

Two persons A and B start from the same point. A walks 14 m South, then 9 m East. B walks 11 m West, then 7 m West. What is the distance between them?
Step-by-step:
1. A's final position: (9, -14)
2. B's final position: (-18, 0)
3. Distance = √[(9--18)² + (-14-0)²] = √[27² + -14²] = 30 m
two-persons, relative, distance

Question 6

Two runners start from the same point on a circular track of length 518 m. Their speeds are 8 m/s and 12 m/s. If they run in the same direction, when will they meet again?
Step-by-step:
1. Relative speed (same direction) = |12 - 8| = 4 m/s
2. Time to meet = Track length / Relative speed = 518 / 4 = 129.5 seconds
circular, track, meeting, laps

Question 7

A person walks 14 m South, then 25 m West, then 14 m West, then 19 m East. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: -14 m South
- East-West: -20 m West
2. Displacement = √(-20² + -14²) = √596 = 24 m
3. Total distance walked = 72 m
multi-stage, displacement, complex

Question 8

From point P, a person walks 8 m West, then 6 m South. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(8² + 6²)
3. = √(64 + 36) = √100 = 10 m
pythagoras, right-angle, shortest-distance

Question 9

A runner runs at 5 m/s on a circular track of length 744 m for 180 seconds. How many laps does he complete?
Step-by-step:
1. Distance covered in 180 seconds = 5 × 180 = 900 m
2. Number of laps = Distance / Track length = 900 / 744 = 1.2 laps
circular, track, meeting, laps

Question 10

A person walks 20 m South, then 12 m West, then 20 m North, then 15 m South. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: -15 m South
- East-West: -12 m West
2. Displacement = √(-12² + -15²) = √369 = 19 m
3. Total distance walked = 67 m
multi-stage, displacement, complex

Question 11

A 155 cm tall person casts a 167 cm shadow. A nearby building is 867 cm tall. How long will its shadow be?
Step-by-step:
1. Ratio of height to shadow length = 155/167 = 0.93
2. For object: Height / Shadow = 0.93
3. Shadow = Height / Ratio = 867 / 0.93 = 934.1 cm
shadow, similar-triangles, ssc

Question 12

A boat travels 72 km downstream in 5.5 hours and upstream in 10.3 hours. The stream speed is 3 km/h. Find the boat's speed in still water.
Step-by-step:
1. Let boat speed = x km/h, stream speed = 3 km/h
2. Downstream: 72/(x + 3) = 5.5
3. Upstream: 72/(x - 3) = 10.3
4. Solving gives x = 10 km/h
boat, stream, upstream, downstream

Question 13

A person walks 12 m West, then 13 m South, then 13 m West, then 25 m South. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: -38 m South
- East-West: -25 m West
2. Displacement = √(-25² + -38²) = √2069 = 45 m
3. Total distance walked = 63 m
multi-stage, displacement, complex

Question 14

From point P, a person walks 8 m North, then 6 m East. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(8² + 6²)
3. = √(64 + 36) = √100 = 10 m
pythagoras, right-angle, shortest-distance

Question 15

A person starts from point O and walks 25m South, then 22m East, then 12m South. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 25m South, then 22m East, then 12m South
2. Net position: (22, -37)
3. Distance = √(22² + -37²) = √1853 = 43 m
basic, movement, straight-line

Question 16

Two runners start from the same point on a circular track of length 639 m. Their speeds are 7 m/s and 13 m/s. If they run in the same direction, when will they meet again?
Step-by-step:
1. Relative speed (same direction) = |13 - 7| = 6 m/s
2. Time to meet = Track length / Relative speed = 639 / 6 = 106.5 seconds
circular, track, meeting, laps

Question 17

From point P, a person walks 7 m North, then 24 m East. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(7² + 24²)
3. = √(49 + 576) = √625 = 25 m
pythagoras, right-angle, shortest-distance

Question 18

A person starts from point O and walks 11m South, then 15m East. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 11m South, then 15m East
2. Net position: (15, -11)
3. Distance = √(15² + -11²) = √346 = 19 m
basic, movement, straight-line

Question 19

A person walks 21 m East, then 19 m North, then 23 m West, then 19 m South. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 0 m 0
- East-West: -2 m West
2. Displacement = √(-2² + 0²) = √4 = 2 m
3. Total distance walked = 82 m
multi-stage, displacement, complex

Question 20

A 175 cm tall person casts a 101 cm shadow. A nearby building is 599 cm tall. How long will its shadow be?
Step-by-step:
1. Ratio of height to shadow length = 175/101 = 1.73
2. For object: Height / Shadow = 1.73
3. Shadow = Height / Ratio = 599 / 1.73 = 345.7 cm
shadow, similar-triangles, ssc
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