48
Motion in opposite directions
Textbook: Part 2, lesson 48, pp. 28–30
GoalMotion towards each other: approach speed and meeting.
New words
motion in opposite directions · qarama-qarshi harakatapproach speed · yaqinlashish tezligiremaining distance · qolgan masofameeting · uchrashuv
Explanation
If two objects set out at the same time towards each other, the distance between them shrinks every hour by v₁ + v₂; this is the approach speed: v_app = v₁ + v₂. After t hours the distance left is S − (v₁ + v₂) × t. When it becomes 0 they meet. For example, walkers 36 km apart at 4 and 5 km/h meet after 36 : (4 + 5) = 4 h.
Worked examples
Approach speed 4 + 5 = 9 km/h; 36 : 9 = 4 h.
From towns 350 km apart at 60 and 80 km/h towards each other: after 2 h, 350 − (60 + 80) × 2 = 70 km are left.
Class activity
“Meeting”: two children walk towards each other from opposite ends of the classroom at a normal pace; add their step counts to estimate the distance.
Practice
1
Two walkers go towards each other at 4 km/h and 5 km/h. What is the approach speed in km/h?
9
2
Two walkers set out from places 36 km apart at 4 and 5 km/h towards each other. After how many hours do they meet?
4
3
Two cars leave towns 350 km apart at the same time and drive towards each other at 60 and 80 km/h. How many km apart are they after 2 h?
70
4
Two cyclists rode towards each other at 15 and 12 km/h and met after 3 h. What was the starting distance in km?
81