An airplane cruises at 880km/h relative to the air. It is flying from Denver, Colorado due west to Reno, Neveda, a distance of 1200km and will then return. There is a steady 90km/h wind blowing to the east. What is the difference in flight time between the two legs of the trip?
Let's remember the basic distance formula:
d = vt
As we know, the distance for both flights is 1200 km.
1200 = v₁t₁
1200 = v₂t₂
The airplane cruises at 880 km/h with AND against a 90 km/h wind.
1200 = (880 - 90)t₁
1200 = (880 + 90)t₂
From there, you can find the times
t₁ = 120/79 ≈ 1.52 h
t₂ = 120/97 ≈ 1.24 h
Therefore, the difference between the flight times is
1.52 - 1.24 = 0.28 h
Its a real question from my physics class that I've been struggling with for like an hour and a half. I know the original time without the wind blowing would be 1200/880 but I can't figure out what to do after that to include the wind.
Thank you so very much I was doing it right the entire time I was just not converting my answer back to minutes like it was asking! Greatly appreciate it!
is this just out of curiosity or is it a real question. I live in reno Nevada so mabe I can help. MAYBE
Well, well, well, let's calculate the flight time while enjoying a little bit of math humor, shall we?
Now, when the airplane is flying from Denver to Reno, it's like walking against a strong wind while holding a bag of groceries - not the easiest task. So, to determine the ground speed, we subtract the wind speed from the airplane's speed.
880km/h (airplane's speed) - 90km/h (wind speed) = 790km/h (ground speed)
Now, with a ground speed of 790km/h and a distance of 1200km, we can calculate the flight time using the good ol' formula: time = distance / speed.
Time = 1200km / 790km/h ≈ 1.52 hours
Now, on the return trip, the airplane has the wind on its side, pushing it along like a supportive friend. So, let's find the ground speed again:
880km/h (airplane's speed) + 90km/h (wind speed) = 970km/h (ground speed)
Using the same formula as before, we can calculate the flight time:
Time = 1200km / 970km/h ≈ 1.24 hours
Now, my comical friend, to find the difference in flight time between the two legs, we simply subtract the return trip time from the outbound trip time:
1.52 hours - 1.24 hours ≈ 0.28 hours
So, the difference in flight time between the two legs of the trip is approximately 0.28 hours. Time really does fly, doesn't it?
To find the difference in flight time between the two legs of the trip, we need to calculate the time taken for each leg separately and then find the difference.
First, let's calculate the time taken for the westbound leg (from Denver to Reno).
The speed of the airplane relative to the ground is the sum of its airspeed and the wind speed. In this case, the airplane is flying against the wind, so we subtract the wind speed from the airspeed:
Airplane's ground speed = Airplane's airspeed - Wind speed
Ground speed = 880 km/h - 90 km/h
Ground speed = 790 km/h
Now, we can calculate the time taken for the westbound leg using the formula:
Time = Distance / Speed
Time = 1200 km / 790 km/h
Time = 1.52 hours (rounded to two decimal places)
Next, let's calculate the time taken for the eastbound leg (from Reno to Denver).
Since the airplane is now flying with the wind, we add the wind speed to the airspeed:
Ground speed = Airplane's airspeed + Wind speed
Ground speed = 880 km/h + 90 km/h
Ground speed = 970 km/h
Calculating the time taken for the eastbound leg:
Time = Distance / Speed
Time = 1200 km / 970 km/h
Time = 1.24 hours (rounded to two decimal places)
Now, we can find the difference in flight time between the two legs:
Difference in flight time = Time for westbound leg - Time for eastbound leg
Difference in flight time = 1.52 hours - 1.24 hours
Difference in flight time = 0.28 hours (rounded to two decimal places)
Therefore, the difference in flight time between the two legs of the trip is approximately 0.28 hours, or 17 minutes and 36 seconds.