Solve Aeroplane Problem: Find Time t for Strike

  • Thread starter Cathartics
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In summary, the conversation discusses a problem involving a pilot flying a plane horizontally at a constant velocity and at a certain height above ground. The pilot then encounters a sloped ground and the question is asked at what time will the plane strike the ground if the heading is not changed. The solution involves using the formula x=vt and considering the constant velocity of the plane. A discussion also takes place about understanding the logic behind using this formula.
  • #1
Cathartics
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[SOLVED] Aeroplane problem!

A pilot flies horizontally at 1350 km/h, at height h = 50 m above initially level ground. However, at time t = 0, the pilot begins to fly over ground sloping upward at angle θ = 4.3°. If the pilot does not change the airplane's heading, at what time t does the plane strike the ground?

Here is what i tired to do

I took tan4.3 = 50/x and found x =664.98 and then tried to find time(t) by using this formula
x = ((v1-v2) * t / 2 ) where v1 = initial velocity and v2 = final velocity but when i plug em up online they tell me it's wrong. Please help!
 
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  • #2
The velocity of the plane is constant. Just use x=vt.
 
  • #3
Cathartics said:
I took tan4.3 = 50/x and found x =664.98

That part is fine.

and then tried to find time(t) by using this formula
x = ((v1-v2) * t / 2 ) where v1 = initial velocity and v2 = final velocity

Think about it for a second. The velocity isn't changing. That means that the initial and final velocities must be the same. All you have to do is figure out how long it takes the plane to travel 664.98m at 1350 km/h (watch your units - the distance is in m, but the speed is in km/h).
 
  • #4
Many thanks!

Thanks shooting_star, I got that right. And thank you tom for that info but x=vt did the trick...
 
  • #5
Tom wanted to you arrive at the x=vt through some logic, which would have helped you the next time. I do hope you know why or how or when we use that formula.
 

1. What is the "aeroplane problem" and why is it important to solve?

The "aeroplane problem" refers to the scenario of an aeroplane being struck by a bolt of lightning while in flight. It is important to solve because it poses a safety risk to the passengers and crew on board the plane, and understanding the time it takes for the strike to occur is crucial for developing safety protocols.

2. How do scientists determine the time it takes for a lightning strike to hit an aeroplane?

Scientists use mathematical equations and simulations to calculate the time it takes for a lightning strike to hit an aeroplane. These calculations take into account factors such as the speed of the plane, the distance between the plane and the lightning strike, and the speed of the lightning bolt itself.

3. Can the time for a lightning strike to hit an aeroplane be predicted accurately?

While scientists can use mathematical models to estimate the time for a lightning strike to hit an aeroplane, it is difficult to predict with 100% accuracy. This is because lightning is a natural phenomenon and can be affected by various factors such as weather conditions and the exact trajectory of the plane.

4. How can understanding the time for a lightning strike to hit an aeroplane improve air travel safety?

By understanding the time it takes for a lightning strike to hit an aeroplane, safety protocols can be established to minimize the risk to passengers and crew. This could include avoiding flying in areas with high lightning activity, implementing lightning protection measures on planes, and using real-time weather data to adjust flight paths.

5. Is there ongoing research to improve our understanding of the "aeroplane problem"?

Yes, there is ongoing research and development in the field of lightning protection for aircraft. Scientists are constantly working to improve our understanding of lightning strikes and to develop new technologies and strategies to prevent lightning strikes from damaging planes and harming passengers and crew.

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