Question

12 a bird flies parralell to a railway track at a speed of 60 km/h. what is the speed of the bird as observed by a passenger in a coach of a train moving on the track in the same direction as the bird at a speed of 160km/h?

220 km/h

240 km/h

100 km/h

120 km/h



13 a driver does a round trip to ibadan from lagos, returning to his take-off point in five hours. the distance of ibadan from lagos is 130 km. what is his average velocity?

52 km/h

26 km/h

0 km/h

104 km/h



14 a booat can travel at a speed of 12 km/h on still water of a river. when the river is flowing at a speed of 3 km/h the boat can also travel at a speed of 3 km/h relative to the water in the river. a boatman using this boat aims to cross the river from point a on the river bank to point b directly opposite to point a on the other bank of the river. how should he aim the boat to achieve this goal?

75.5 degrees upstream

14.5 degrees downstream

75.5 degrees downstream

14.5 degrees upstream

Answer 1

Answer on Question#56259 - Physics - Relativity

12. A bird flies parallel to a railway track at a speed of $v_{b} = 60\frac{\mathrm{km}}{\mathrm{h}}$ . What is the speed of the bird as observed by a passenger in a coach of a train moving on the track in the same direction as the bird at a speed of $v_{t} = 160\frac{\mathrm{km}}{\mathrm{h}}$ ?

220 km/h

240 km/h

100 km/h

120 km/h

13. A driver does a round trip to Ibadan from Lagos, returning to his take-off point in five hours. The distance of Ibadan from Lagos is $130\mathrm{km}$ . What is his average velocity?

52 km/h

26 km/h

0 km/h

104 km/h

14. A boat can travel at a speed of $12 \, \text{km/h}$ on still water of a river. When the river is flowing at a speed of $3 \, \text{km/h}$ the boat can also travel at a speed of $3 \, \text{km/h}$ relative to the water in the river. A boatman using this boat aims to cross the river from point a on the river bank to point b directly opposite to point a on the other bank of the river. How should he aim the boat to achieve this goal?

75.5 degrees upstream

14.5 degrees downstream

75.5 degrees downstream

14.5 degrees upstream

Solution:

12. In the system of reference of the train bird flies with velocity

$$v _ {b} ^ {\prime} = v _ {b} - v _ {t} = 1 6 0 \frac {\mathrm {k m}}{\mathrm {h}} - 6 0 \frac {\mathrm {k m}}{\mathrm {h}} = - 1 0 0 \frac {\mathrm {k m}}{\mathrm {h}}$$

Therefore the bird's speed in this system of reference is $100\frac{\mathrm{km}}{\mathrm{h}}$ .

13. Since the average velocity is given by the full displacement divided by the time of the trip, driver's average velocity is $0\frac{\mathrm{km}}{\mathrm{h}}$ . He returned to the same position after 5h (displacement is zero).

14. His speed in the direction opposite to the direction of water flow must be $v_{\parallel} = 3 \frac{\mathrm{km}}{\mathrm{h}}$ to compensate the displacement due to river flow. His speed in direction to the point on the other bank of the river is $v_{\perp} = 12 \frac{\mathrm{km}}{\mathrm{h}}$. This two speeds are related to the direction angle $\alpha$ by the following relation

$$\tan \alpha = \frac {v _ {\perp}}{v _ {\parallel}}$$

Therefore

$$\alpha = \atan \frac {v _ {\perp}}{v _ {\parallel}} = \atan \frac {12}{3} = 75.5{}^{\circ}$$

**Answer:**

12. $100 \frac{\mathrm{km}}{\mathrm{h}}$

13. $0 \frac{\mathrm{km}}{\mathrm{h}}$

14. $75.5{}^{\circ}$

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