Chapter 2: Two Objects Moving in the Same Direction

Transcription

1 Chapter 2 : Two Objects Moving in the Same Direction Solutions to Problems involving Two Objects Moving in the Same Direction: 1. Same Distance: Lorry 60 2u Car 90 3u Time 3p 2p (3p 2p) 45 mins 1p 45 mins Consider Lorry: 3p (3 x 45 mins) = 135 mins = 2.25 h 1d (60 km/h x 2.25 h) = 135 km 5d (5 x 135 km) = 675 km The distance is 675 km. 1

2 2. Same Distance: M 3u 7u Time 3.5 7p C 1.5 3p a) (7u 3u) 60 km/h 4u 60 km/h 1u (60 km/h 4) = 15 km/h Consider motorcyclist: 3u (3 x 15 km/h) = 45 km/h b) Consider Car: 7u (7 x 15 km/h) = 105 km/h Distance after 1.5 h (105 km/h x 1.5 h) = km Total Distance ( ) km = km a) The motorcyclist s speed was 45 km/h. b) The distance was km. 2

3 3. Same Distance: Z 88 8u T 99 9u Time 9p 8p a) (9p 8p) 15 mins 1p 15 mins Consider Zen: 9p (9 x 15 mins) = 135 mins = 2.25 h Distance (88 km/h x 2.25 h) = 198 km b) Consider Tim: 8p (8 x 15 mins) = 120 mins = 2 h 10:00am + 15 min + 2hr = 12:15pm a) The distance was 198 km. b) Tim reached City B at 12:15pm. 3

4 4. Same Time: A 225 5u B 135 3u Distance 5p 3p (5p + 3p) 2700 m 1p (2700 m 8) = m Consider Bernice: 3p (3 x m) = m 1d ( ) m = m 2d (2 x m) = m The distance was m. 4

5 5. Same Time: S 88 11u J 96 12u Distance 11p 12p (12p 11p) 7 km 1p 7 km Consider Jimmy: 12p (12 x 7 km) = 84 km Total distance ( ) km = 99 km The distance was 99 km. 5

6 6. (B & C) Same Time: B u C u Distance 15p 14p (15p 14p) 3 km 1p 3 km Consider Car B: 15p (15 x 3 km) = 45 km (45 km 150 km/h) = 0.3 h = 18 mins 10:15am + 18 mins = 10:33am Car B overtook Car C at 10:33 am. 6

7 7. Same Time: A K 7u 10u Distance 7p 10p (10p 7p) 1800 m 3p 1800 m 1p (1800 m 3) = 600 m Consider Karen: 10p (10 x 600 m) = 6000 m (6000 m 10 m/s) = 600 s = 10 min 11:00am + 10 mins = 11:10am Karen caught up with Alice at 11:10am. 7

8 8. Same Time: S 96 4u T 72 3u Distance 4p 3p (4p 3p) 20 km 1p 20 km Consider Tom: 3p (3 x 20 km) = 60 km (60 km 72 km/h) = 6 5 h = 50 mins 6:00pm + 50 mins = 6:50 pm Steven overtook Tom at 6:50 pm. 8

9 9. Same Time: S 90 9u C 50 5u Distance 9p 5p 5p 20 km 1p (20 km 5) = 4 km 7p (7 x 4 km) = 28 km The distance is 28 km. 9

10 10* Case 1: Consider (T & B) Same Time: A 63 7u B 9 1u Distance 7p 1p 1p 2.8 km 3p (3 x 2.8 km) = 8.4 km 10

11 Case 2: Consider (T & H) Same Time: T 63 9u H 7 1u Distance 9p 1p 14 1 (9p 1p) ( ) km = 9 3 km 8 p km 1p (9 3 1 km 8) = km 1 ( ) km = 2.1 km Harry walks 2.1 km. 11

12 11. Case 1: Difference (200 m 50 s) = 4 m/s Case 2: Same Distance: 3u 2u Time J 40 2p P 60 3p (3u 2u) 4 m/s 1u (12 m/s 3) = 4 m/s 3u (3 x 4 m/s) = 12 m/s 2u (2 x 4 m/s) = 8 m/s Jason s speed is 12 m/s and Philip s speed is 8 m/s 12

13 12. a) (105 km h) = 90 km/h b) (18 km 90 km/h) = 5 1 h = 12 mins 11:15am 12 mins = 11:03am a) Leon s speed was 90 km/h. b) Leon started at 11:03 am. 13

14 13. 4d 4 km 1d (4 km 4) = 1 km 9d (9 x 1 km) = 9 km (9 km 12 km/h) = 4 3 h = 45 mins Martin took 45 minutes. 14