TOPIC QUESTION BANK // MATHS

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Maths

What is the conversion method for wind speed from m/s to kt?

To quickly convert wind speed from m/s to kt, you can use the following rule of thumb:

kt ≈ m/s × 2

Example:

10 m/s ≈ 20 kt

Fuel flow is 2200 kg/h and groundspeed is 300 kt.
How much fuel will be burned over a distance of 180 NM?

Step 1 – Calculate the time:
Time = Distance / Groundspeed
→ 180 ÷ 300 = 0.6 h

Step 2 – Multiply by fuel flow:
Fuel = Fuel flow × Time
→ 2200 × 0.6 = 1320 kg

✅ You will burn approximately 1320 kg of fuel over 180 NM at a groundspeed of 300 kt and fuel flow of 2200 kg/h.

Engine failure scenario (jet aircraft):
Fuel flow = 2400 kg/h
Fuel onboard = 5000 kg
Groundspeed = 270 kt

What is the approximate maximum distance you can fly before getting into the 30 minutes of final reserves?

Step 1 – Calculate total endurance:
5000 ÷ 2400 ≈ 2.08 h

Step 2 – Subtract 0.5 h of final reserve:
2.08 – 0.5 = 1.58 h available before final reserves

Step 3 – Multiply by groundspeed to get distance:
1.58 × 270 ≈ 427 NM

✅ You can fly approximately 427 NM before reaching the final 30 minutes of fuel reserve.

An aircraft is cruising at FL340 and is cleared to descend to FL260, to be level 10 NM before a specific waypoint.
Average groundspeed is 360 kt and the descent rate is 1800 ft/min.

How many nautical miles before the waypoint should the descent be initiated?

Step 1 – Altitude to lose:
FL340 – FL260 = 8,000 ft

Step 2 – Time to descend:
8,000 ÷ 1800 ≈ 4.44 minutes

Step 3 – Distance covered at 360 kt:
(360 ÷ 60) × 4.44 ≈ 6 × 4.44 = 26.7 NM

Step 4 – Add the 10 NM buffer:
26.7 + 10 = 36.7 NM

Arrondi : 37 NM

✅ The descent should begin approximately 37 NM before the waypoint to be level 10 NM in advance.

Aircraft A and aircraft B are cruising toward each other at FL330 and FL340 respectively.
– Aircraft A groundspeed: 400 kt
– Aircraft B groundspeed: 500 kt
– Distance between them: 1800 NM

After how much time will they cross each other?

Step 1 – Combine both groundspeeds:
400 + 500 = 900 kt

Step 2 – Time = Distance / Relative speed:
1800 ÷ 900 = 2.0 hours

✅ The aircraft will cross each other after 2 hours.

An aircraft is cruising at FL300 and is cleared to descend to FL120, to be level by a specific waypoint.
Average groundspeed is 300 kt and the descent rate is 1500 ft/min.

How many nautical miles before the waypoint should the descent be initiated?

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What is your average groundspeed if you cover 180 NM in 1.2 hours?

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You are flying at a groundspeed of 120 kt. How long will it take you to cover a distance of 90 NM?

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You are flying at a groundspeed of 140 kt. How many nautical miles will you cover in 30 minutes?

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After flying 80 NM, an aircraft is 4 NM off-track.
The next waypoint is 40 NM ahead.
What heading correction should be applied to rejoin the intended track by the waypoint?

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