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You are in an airplane climbing at 750 ft/min. If your ground speed is 90 MPH, by how much will you clear the mountain in front of you that is 10 miles away and 5000 feet above your altitude?

user40543
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    At 90MPH, how many feet/minute are you covering? Multiply that by 750 then subtract 5000. #HomeworkHelp – FreeMan May 21 '19 at 20:17
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    What did you try? Where did you encounter difficulty? – abelenky May 21 '19 at 21:20
  • Basic rise-over-run algebra, or speed-distance-time. https://www.timecalculator.net/speed-distance-time-calculator – ivanivan May 21 '19 at 21:36
  • My calculator says you are going to die – MikeY May 21 '19 at 22:39
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    Welcome to aviation.SE! You will get a much better response to questions like this if you also tell us what your problem or confusion is with the question. The [tour] be helpful if you're new to StackExchange. – Pondlife May 21 '19 at 22:48

2 Answers2

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So, 5,000 feet to gain and you're climbing at 750 ft/min. At that rate it would take 5000/750=6.67 minutes (to 2 decimal places) to make it.

A speed of 90 MPH is 1.5 miles per minute. Thus 10 miles at that speed would be 10/1.5=6.67 minutes. Hmm, same value. I would suggest turning slightly to avoid the peak.

Seriously, the difficulty is that you can't depend on the kind of precision seemly presented by the the simplicity of the problem as stated. Here are a few things that I can think of offhand that need to be taken into account:

  • First, just to clear up a units consideration that bothers the likes of me with an nitpicking mind, whomever wrote the question would be better of stating the distance in either nautical miles or kilometers rather than statute miles and their respective speeds. Aviation no longer uses statute miles to speak of.
  • Depending on the aircraft, you might not be able to maintain the starting rate of climb as you gain altitude. Normally aspirated engines typically lose available power with a gain of altitude.
  • In the real world, there is always wind overall, and it changes with altitude. If that wind overall was a headwind, that would help you clear the mountain. HOWEVER, climbing toward a mountain on it's leeward side, especially if it is part of a ridge system, invites having to contend with serious downdrafts (and if there's a lenticular cloud over the peak, don't even think of it).
  • It's unrealistic to depend on your groundspeed to remain constant.

So, while the theoretical answer to the question is that you will have 0 (that's zero) clearance, unless my 80 year-old brain is again malfunctioning, the practical answer is that you should clear all high terrain by, say, a thousand feet or more, and always leave yourself a way to turn toward lower terrain.

Terry
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1. At 90 MPH How long will it take to go 10 miles?

$ \frac{60\:minutes}{90\:miles} \cdot 10\:miles \ = 6\colon40\: minutes$

2. How much altitude will you gain in 6:40, at 750fpm?

$6 \frac{2}{3}minutes \cdot \frac{750 feet}{minute} = 5,000\:feet$

3. If you gained 5,000 feet, by how much will you clear the mountain in front of you?

You're not going to make it.

abelenky
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  • Agree with the conclusion (even Bald Mountain). However 2 things were left out. 1. Loss of performance with climb. Increase in true airspeed with climb. Factoring both in, I'd go for a climbing turn to a different course. – Robert DiGiovanni May 21 '19 at 21:53