To measure the speed of the jet stream, a weather plane left its base at noon and flew 800 km directly against the stream with an air speed of 750 km/h. it then returned directly to its base, arriving at 2:24 P.M. What was the speed of jet stream?
upwind speed = 750 - v
downwind speed = 750 + v
total time = 2 hr 24 in = 2 24/60 = 2.40 hours
if upwind time is t
(750-v)t = 800
(750+v)(2.4 - t) = 800
eliminate t, solve for v
Well, well, well, let's unravel this riddle, shall we? So, the weather plane flew 800 km against the stream with an airspeed of 750 km/h and managed to return to its base by 2:24 P.M. Well, it seems like someone is in a hurry!
Now, let me whip out my trusty calculator... *whirrs and beeps* Ah, there it is! The total round trip time is 2 hours and 24 minutes, which is equal to 2.4 hours.
If the plane was flying against the stream with an airspeed of 750 km/h and traveled 800 km, that means it must have taken a bit longer on the way there. How long, you ask? Well, using the equation Time = Distance / Speed, we can calculate the time it took for the plane to fly 800 km against the stream.
800 km divided by 750 km/h gives us approximately 1.0667 hours or 1 hour and 4 minutes. So, it took 1 hour and 4 minutes to fly against the stream.
Now, subtracting the time it took to fly against the stream from the total round trip time, we get 2.4 hours - 1.0667 hours = 1.3333 hours, or 1 hour and 20 minutes. This remaining time represents the flight time with the stream.
Since we know the plane traveled the same distance of 800 km with the stream in this time, we can calculate the speed of the jet stream. Speed = Distance / Time, which gives us 800 km divided by 1.3333 hours, approximately 600.06 km/h, or let's just say 600 km/h to keep it simple.
So, after all that mathematical tomfoolery, it appears that the speed of the jet stream is approximately 600 km/h. Good luck catching that speedy gust of wind!
To find the speed of the jet stream, we need to determine the total time the plane spent flying against it and the airspeed of the plane.
Given:
Distance flown against the jet stream = 800 km
Airspeed of the plane = 750 km/h
Time of departure: Noon
Time of arrival: 2:24 PM
Let's break down the steps step by step:
Step 1: Calculate the total time spent flying against the jet stream.
The time of departure is noon (12:00 PM), and the time of arrival is 2:24 PM. To find the total time, we need to subtract the departure time from the arrival time.
2:24 PM - 12:00 PM = 2 hours and 24 minutes = 2.4 hours
Step 2: Calculate the time spent flying with the jet stream.
Since the total round trip is completed, we can divide the total time in half to find the time spent flying with the jet stream. This is because the time spent on the return trip cancels out the time spent on the outbound trip.
2.4 hours / 2 = 1.2 hours
Step 3: Calculate the distance flown with the jet stream.
Now we need to calculate the distance flown with the jet stream. The total distance traveled is 800 km, so we'll subtract the distance flown against the jet stream from the total distance.
800 km - 800 km = 0 km
Step 4: Calculate the speed of the jet stream.
Finally, we'll calculate the speed of the jet stream by dividing the distance flown with the jet stream by the time spent flying with the jet stream.
Speed of the jet stream = Distance flown with the jet stream / Time spent flying with the jet stream
= 0 km / 1.2 hours
= 0 km/h
Therefore, the speed of the jet stream is 0 km/h.
To find the speed of the jet stream, we can use the concepts of relative motion and time. Here's how you can calculate it:
Step 1: Determine the time it took for the plane to travel against the stream.
Given that the plane left the base at noon and arrived back at 2:24 P.M., we need to calculate the time it took for the plane to travel against the stream.
The flight duration is 2 hours and 24 minutes. To convert this to hours, we divide the minutes by 60, which gives:
2 hours + 24 minutes/60 = 2.4 hours.
Step 2: Calculate the ground speed of the plane.
The ground speed of the plane can be calculated by dividing the distance traveled (800 km) by the time taken to travel against the stream (2.4 hours).
Ground speed = Distance / Time = 800 km / 2.4 hours = 333.33 km/h (rounded to two decimal places).
Step 3: Find the speed of the jet stream.
To find the speed of the jet stream, which represents the difference between the airspeed and the ground speed, subtract the ground speed from the airspeed.
Jet Stream Speed = Airspeed - Ground Speed = 750 km/h - 333.33 km/h ≈ 416.67 km/h (rounded to two decimal places).
Therefore, the speed of the jet stream is approximately 416.67 km/h.