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Distance Logic - Advanced Level: net displacement ADVANCED

Master distance logic concepts through this hard problem set practice set. Worksheet 26 of 30 contains 20 advanced-level problems. Deep dive into net displacement while learning distance measurement, relative distances, path length. Recommended for advanced learners aiming for complex scenarios and multi-step problems.

📝 Worksheet 26 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Distance Logic
Worksheet 26 of 30 (86% complete)

Question 1

A person walks 15 m South, then 11 m East, then 15 m North. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 0 m 0
- East-West: 11 m East
2. Displacement = √(11² + 0²) = √121 = 11 m
3. Total distance walked = 41 m
multi-stage, displacement, complex

Question 2

A 150 cm tall person casts a 285 cm shadow. A nearby building is 704 cm tall. How long will its shadow be?
Step-by-step:
1. Ratio of height to shadow length = 150/285 = 0.53
2. For object: Height / Shadow = 0.53
3. Shadow = Height / Ratio = 704 / 0.53 = 1337.6 cm
shadow, similar-triangles, ssc

Question 3

Two runners start from the same point on a circular track of length 590 m. Their speeds are 7 m/s and 14 m/s. If they run in the same direction, when will they meet again?
Step-by-step:
1. Relative speed (same direction) = |14 - 7| = 7 m/s
2. Time to meet = Track length / Relative speed = 590 / 7 = 84.3 seconds
circular, track, meeting, laps

Question 4

A train 241 m long is running at 64 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 64 km/h = 17.8 m/s
2. Time = Length / Speed = 241 / 17.8 = 13.6 seconds
train, platform, pole, ssc

Question 5

Two persons A and B start from the same point. A walks 17 m South, then 20 m East, then 8 m South. B walks 13 m South, then 20 m North, then 6 m North. What is the distance between them?
Step-by-step:
1. A's final position: (20, -25)
2. B's final position: (0, 13)
3. Distance = √[(20-0)² + (-25-13)²] = √[20² + -38²] = 43 m
two-persons, relative, distance

Question 6

A person starts from point O and walks 6m South, then 24m West, then 21m North. What is his straight line distance from point O?
Step-by-step:
1. Track movements: 6m South, then 24m West, then 21m North
2. Net position: (-24, 15)
3. Distance = √(-24² + 15²) = √801 = 28 m
basic, movement, straight-line

Question 7

A boat travels at 14 km/h in still water. Stream speed is 4 km/h. What is the difference between upstream and downstream time for 59 km?
Step-by-step:
1. Downstream speed = 18 km/h, Time = 3.3 hours
2. Upstream speed = 10 km/h, Time = 5.9 hours
3. Difference = 5.9 - 3.3 = 2.6 hours
boat, stream, upstream, downstream

Question 8

Two persons A and B start from the same point. A walks 20 m South, then 6 m West, then 6 m South. B walks 11 m North, then 8 m West, then 8 m West. What is the distance between them?
Step-by-step:
1. A's final position: (-6, -26)
2. B's final position: (-16, 11)
3. Distance = √[(-6--16)² + (-26-11)²] = √[10² + -37²] = 38 m
two-persons, relative, distance

Question 9

A car travels at 30 km/h for 3 hours. What distance does it cover?
Distance = Speed × Time = 30 × 3 = 90 km
speed, time, basic

Question 10

From point P, a person walks 9 m West, then 12 m South. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(9² + 12²)
3. = √(81 + 144) = √225 = 15 m
pythagoras, right-angle, shortest-distance

Question 11

A boat travels 59 km downstream in 3.1 hours and upstream in 4.5 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: 59/(x + 3) = 3.1
3. Upstream: 59/(x - 3) = 4.5
4. Solving gives x = 16 km/h
boat, stream, upstream, downstream

Question 12

From point X, a person goes 5 m East, then 12 m North. What is the shortest distance from point X?
Step-by-step:
1. The path forms a right triangle
2. Shortest distance = √(5² + 12²) = √169 = 13 m
shortest-path, pythagoras

Question 13

A person walks 18 m East, then 25 m North, then 14 m North, then 15 m North. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 54 m North
- East-West: 18 m East
2. Displacement = √(18² + 54²) = √3240 = 57 m
3. Total distance walked = 72 m
multi-stage, displacement, complex

Question 14

From point X, a person goes 5 m East, then 12 m North. What is the shortest distance from point X?
Step-by-step:
1. The path forms a right triangle
2. Shortest distance = √(5² + 12²) = √169 = 13 m
shortest-path, pythagoras

Question 15

Car A at 41 km/h and Car B at 71 km/h start from the same point in the same direction. How long will it take for them to be 388 km apart?
Step-by-step:
1. Relative speed when moving in same direction = |71 - 41| = 30 km/h
2. Time = Distance / Relative Speed = 388 / 30 = 12.9 hours
3. The second car will be 388 km ahead after 12.9 hours
relative, meeting, catch-up

Question 16

From point P, a person walks 3 m South, then 4 m West. What is the shortest distance from point P?
Step-by-step:
1. These movements form a right angle
2. Shortest distance = √(3² + 4²)
3. = √(9 + 16) = √25 = 5 m
pythagoras, right-angle, shortest-distance

Question 17

A train 325 m long is running at 46 km/h. How long will it take to cross a pole?
Step-by-step:
1. Speed = 46 km/h = 12.8 m/s
2. Time = Length / Speed = 325 / 12.8 = 25.4 seconds
train, platform, pole, ssc

Question 18

Train A at 47 km/h and Train B at 72 km/h start from stations 418 km apart and move towards each other. How long will they take to meet?
Step-by-step:
1. Relative speed when moving towards each other = 47 + 72 = 119 km/h
2. Time = Distance / Relative Speed = 418 / 119 = 3.5 hours
relative, meeting, catch-up

Question 19

A person walks 19 m North, then 13 m East, then 15 m South, then 19 m West. Find his displacement from the starting point.
Step-by-step:
1. Track net displacement:
- North-South: 4 m North
- East-West: -6 m West
2. Displacement = √(-6² + 4²) = √52 = 7 m
3. Total distance walked = 66 m
multi-stage, displacement, complex

Question 20

A 150 cm tall person casts a 264 cm shadow. A building casts a 488 cm shadow at the same time. How tall is the building?
Step-by-step:
1. Ratio of shadow to height = 264/150 = 1.76
2. For object: Shadow / Height = 1.76
3. Height = Shadow / Ratio = 488 / 1.76 = 277.3 cm
shadow, similar-triangles, ssc
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