Find initial velocity using rate of climb

[Rebecca_M]

Hi I need to find the horizontal distance traveled by an aircraft just after take off to a vertical height of 10.7m. The rate of climb is 1920m/min.

I'm not really sure how to approch this question. I think simply it would look like a right angles triangle, I would need an initial velocity (ie just at take off) to work it out?
Thanks for your help!

 

[Delphi51]

Welcome to PF, Rebecca.
It is very important to post the entire question, word for word.
In this case, the angle of takeoff is missing so it cannot be solved.
If, for example, the plane was a Harrier and took off vertically, the horizontal distance would be zero. If it went up at 45 degrees, the horizontal distance would be 10.7 meters.

 

[Rebecca_M]

Thanks for your reply Delphi51, unfortunatly I didn't have a entire question, I was trying to preempt an exam question that I had the next day. The exam question ended up having at take off speed of 385Km/h (at point of lift off) and a rate of climb of 250m/min. I still don't really have an idea how it works.

 

[Delphi51]

Well, that is not perfectly clear but likely means the vertical component of speed is 250 m/minute = 4.17 m/s.
The total speed is 385 km/h = 385*1000m/3600s = 107 m/s.
The angle above horizontal must be θ where sin(θ) = 4.17/107 so θ=2.23 degrees. Using the vertical distance of 10.7 m, we have
tan(2.23) = 10.7/x where x is the horizontal distance.

 

[asteriatic]

I can help you approach this question by using the formula for displacement (d = vt) where d is the distance traveled, v is the initial velocity, and t is the time. In this case, we know the vertical height (10.7m) and the rate of climb (1920m/min). We can use this information to calculate the time it takes for the aircraft to reach a height of 10.7m by dividing the height by the rate of climb (10.7m/1920m/min = 0.0056 min).

Next, we can use the same formula to calculate the horizontal distance traveled by the aircraft in this time. However, we need to convert the rate of climb from meters per minute to meters per second (1920m/min = 32m/s). So, the horizontal distance traveled would be d = vt = (32m/s)(0.0056 min) = 0.1792m.

It is important to note that this calculation assumes a constant rate of climb, and does not take into account factors such as wind resistance or changes in the aircraft's velocity. However, it can provide a rough estimate of the horizontal distance traveled by the aircraft just after take off. I hope this helps!