Qa07 boats and streams
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The document discusses concepts related to boats moving with and against streams. It defines that the speed of a boat or swimmer in still water is their baseline speed, and the speed upstream or downstream is calculated by adding or subtracting the stream speed. Several examples are provided to demonstrate calculating distances and stream speeds given time taken to travel upstream and downstream. Formulas are provided to calculate distances and stream/boat speeds using variables for boat speed, stream speed, and time taken to travel distances with or against the current.
Qa07 boats and streams
- 2. BOATS – 1 • Generally the speed of the boat means the speed of the boat in still water. • Similarly the speed of the swimmer means the speed of the swimmer in still water.
- 3. BOATS - 2 • UPSTREAM If the boat (or the swimmer) moves against the stream, then it is called upstream. If the speed of the boat (or the swimmer) is x and the speed of the stream is y, then upstream speed = x – y. • DOWNSTREAM If the boat (or the swimmer) moves with the stream, then it is called downstream. If the speed of the boat (or the swimmer) is x and the speed of the stream is y, then downstream speed = x + y.
- 4. BOATS – 3
- 5. BOATS - 4 Theorem 1. • A man can row x km/h in still water. If in a stream which is flowing at y km/h, it takes him z hours to row to a place and back, the distance between the two places is 2 2 2 z x y x
- 6. BOATS - 5 • A man can row 12 km/h in still water. If the speed of the stream is 8 km/h, if it takes 3 hours to row to a place and back, find the distance between two places. • Here x = 12. Y = 8 and z = 3. • So the distance is 10 km.
- 7. Boats – 5a
- 8. BOATS - 6 Theorem 2. • A man can row a certain distance downstream in x hours and returns the same distance in y hours. If the stream flows at the rate of z km/h, then the speed of the man in still water is given by z x y y x
- 9. Boats – 6a
- 10. BOATS – 7
- 11. BOATS – 8 • Example A man swims downstream 15 km and upstream 9 km, taking 3 hours each time. What is the velocity of current? • Velocity of current = 1km/hr 15 9 2 3
- 12. BOATS - 9 • A man can row 12 km/h in still water. He takes thrice as long to row up as to row down the river. Find the rate of the stream. • Rate of the stream = 2 1 Speed of manin still water No of times to row up as to row down 13 122 = 6 km/h.
- 13. BOATS -10 1. In one hour, a boat goes 11 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is a) 3 b) 5 c) 8 d) 9
- 14. BOATS -11
- 15. BOATS – 12 • A man can row upstream at 8 kmph and downstream at 13kmph. The speed of the stream is a) 2.5kmph b) 4.2 kmph c) 5 kmph d) 10.5 kmph.
- 16. BOATS - 12
- 17. BOATS – 13 A man rows downstream 32 km and 14km upstream. If he takes 6 hours to cover each distance, then the velocity (in kmph) of the current is a) 0.5 b) 1 c) 1.5 d) 2
- 18. BOATS – 13 A man rows downstream 32 km and 14km upstream. If he takes 6 hours to cover each distance, then the velocity (in kmph) of the current is a) 0.5 b) 1 c) 1.5 d) 2 Rate downstream = 6 32 kmph; Rate upstream = 6 14 kmph. Speed in still water = 6 14 6 32 2 1 kmph = 2 3 kmph = 1.5 kmph.
- 19. BOATS - 14 • 1)A boat running downstream covers a distance of 16km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water? a) 4km/hr b) 6 km/hr c) 8 km/hr d) Data inadequate.
- 20. BOATS – 14 • A boat running downstream covers a distance of 16km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water? a) 4km/hr b) 6 km/hr c) 8 km/hr d) Data inadequate. Rate downstream = 2 16 kmph = 8 kmph; Rate upstream = 4 16 kmph = 4 kmph. Speed in still water = 48 2 1 kmph = 6 kmph.
- 21. BOATS – 15 If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph, then the man’s rate along the current is a) 4.25 kmph b) 6 kmph c) 6.5 kmph d) 8.5 kmph
- 22. BOATS – 15 If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph, then the man’s rate along the current is a) 4.25 kmph b) 6 kmph c) 6.5 kmph d) 8.5 kmph Let the rate along the current be x kmph. Then, 53.5 2 1 x x = 6.5 kmph.