Answer:
x = 5m/s
Step-by-step explanation:
Distance flying out = 12 km (headwind)
Distance flying back = 12 km (tailwind)
total distance = 12 + 12 =24 km
wind speed = 1km/h
speed going out (with headwind) = (x - 1) km/h
speed coming back (with tailwind) = (x + 1) km/h
Time taken to go out = distance going out / speed going out
= 12 / (x-1)
Time taken to come back = distance coming back / speed coming back
= 12 / (x+1)
total time = time taken to go out + time taken to come back
5 =[ 12/(x-1) ] + [ 12/(x-1)]
expanding this, we will get
5x² - 24x - 5 = 0
solving quadratic equation, we will get
x = -1/5 (impossible because speed cannot be negative)
or
x = 5 (answer)
The speed of sparrow in still air is 5 km/hr.
The magnitude of rate of change of position is called speed.
Now it is given that,
speed of a sparrow in still air = x km/hr
speed of wind = 1 km/hr
So, Speed of sparrow in going out = (x-1) km/hr
and Speed of sparrow in going in = (x+ 1) km/hr
Distance travelled by sparrow in going out = 12 km
Distance travelled by sparrow in going in = 12 km
Now, time taken by the sparrow in going out = 12/(x-1) hour
and time taken by the sparrow in going in = 12/(x+ 1) hour
Therefore, Total distance travelled by sparrow = 12 + 12 km = 24km
Since,Total time taken by sparrow in whole flight = 5hour
⇒ 12/(x-1) + 12/(x+ 1) = 5
⇒ 12x - 12 + 12x + 12 = 5x² - 5
⇒ 5x²+ 24x - 5 = 0
Solving the above equation we get x = 5
Hence the speed of sparrow in still air is 5 km/hr.
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