A plane flies at 800km/h in stationary air. The distance to be traveled is 3000km. What was the wind speed if the journey actually takes 4.0 hours?
To find the wind speed, we can use the formula:
Wind Speed = Actual Speed - Stationary Speed
Here, the actual speed is the speed at which the journey takes place, and the stationary speed is the speed of the plane in stationary air.
Given:
Stationary speed of the plane = 800 km/h
Distance to be traveled = 3000 km
Duration of the journey = 4.0 hours
We can calculate the actual speed using the formula:
Actual Speed = Distance / Time
Actual Speed = 3000 km / 4.0 hours
Now, we can substitute the given values into the formula to calculate the actual speed:
Actual Speed = 750 km/h
Finally, we can find the wind speed by subtracting the stationary speed from the actual speed:
Wind Speed = 750 km/h - 800 km/h
Wind Speed = -50 km/h
Since the wind speed is negative, it means that the headwind is blowing in the opposite direction of the plane's motion. Therefore, the wind speed is 50 km/h.
To determine the wind speed, we can use the formula:
Distance = Speed * Time
Given:
Speed of the plane in stationary air = 800 km/h
Distance to be traveled = 3000 km
Time taken for the journey = 4.0 hours
Let's assume the wind speed as 'w'.
Now, let's calculate the effective speed of the plane:
Effective Speed = Speed of the plane in stationary air + Wind speed
Effective Speed = 800 km/h + w
Using the formula mentioned above, we have:
Distance = Effective Speed * Time
3000 km = (800 km/h + w) * 4.0 hours
Simplifying the equation:
3000 km = 3200 km/h + 4w
Subtracting 3200 km/h from both sides:
-200 km/h = 4w
Dividing both sides by 4:
-50 km/h = w
Therefore, the wind speed is -50 km/h. The negative sign indicates that the wind is blowing against the direction of the plane's motion.