Finding the Speed of an Aeroplane - Math Help Forum

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In summary: An aeroplane travels at a certain speed, based on its size and weight. It is important to know this speed so that you can correctly time how long it will take to reach your destination. To find the speed of an aeroplane, you must use the following equation:$v=\sqrt{2g\cdotr}$Where $v$ is the speed of the aeroplane, $g$ is the gravitational force, and $r$ is the distance from the centre of the aeroplane. For example, an aeroplane that is 10 meters in length and has a mass of 100 kilograms will travel at a speed of 400 kilometers per
  • #1
wrightarya
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question is attached.
the answer at the back of the book is 553.6 kmph

this is for my maths homework and I am stuck on this question.:(
 

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  • #2
wrightarya said:
question is attached.
the answer at the back of the book is 553.6 kmph

this is for my maths homework and I am stuck on this question.:(

What have you tried so far?
 
  • #3
If the speed is x km/h then the time taken is 1000/x hours.

If the speed is x-120 then the time taken is 1000/x hours and this is equal to the other time plus 0.5 hours.

i don't know how to form an equation =/
 
  • #4
wrightarya said:
If the speed is x km/h then the time taken is 1000/x hours.

If the speed is x-120 then the time taken is 1000/x hours and this is equal to the other time plus 0.5 hours.

i don't know how to form an equation =/

Actually if the speed is (x - 120) then the speed is 1000/(x - 120).

Now as you have stated, this is equal to the other time plus half an hour, so

$\displaystyle \begin{align*} \frac{1000}{x - 120} &= \frac{1000}{x} + \frac{1}{2} \end{align*}$

Can you now solve for x?
 
  • #5
Prove It said:
Actually if the speed is (x - 120) then the speed is 1000/(x - 120).

Now as you have stated, this is equal to the other time plus half an hour, so

$\displaystyle \begin{align*} \frac{1000}{x - 120} &= \frac{1000}{x} + \frac{1}{2} \end{align*}$

Can you now solve for x?

i tried solving it like this:

1000/x-120 = 2000 + x
1000= (2000+x) (x-120)
1000= x^2 + 1880x - 240000
= x^2 + 1880x - 241000
substituted into quadratic formula
x=120 or -2000

dont know if i did that right, but its not what the answer says in the back of the book...
 
  • #6
wrightarya said:
i tried solving it like this:

1000/x-120 = 2000 + x

No, $\displaystyle \begin{align*} \frac{1000}{x} + \frac{1}{2} \end{align*}$ is not $\displaystyle \begin{align*} 2000 + x \end{align*}$, it's $\displaystyle \begin{align*} \frac{2000 + x}{2x} \end{align*}$, so when you cross multiply you should get

$\displaystyle \begin{align*} \frac{1000}{x - 120} &= \frac{1000}{x} + \frac{1}{2} \\ \frac{1000}{x - 120} &= \frac{2000 + x}{2x} \\ 1000 \left( 2x \right) &= \left( 2000 + x \right) \left( x - 120 \right) \end{align*}$

Go from here...
 
  • #7
wrightarya said:
If the speed is x km/h then the time taken is 1000/x hours.

If the speed is x-120 then the time taken is 1000/x hours and this is equal to the other time plus 0.5 hours.

i don't know how to form an equation =/
Finding speed of an aeroplane - The Student Room

You almost quoted me correctly. ;)
 

FAQ: Finding the Speed of an Aeroplane - Math Help Forum

What is the average speed of an aeroplane?

The average speed of an aeroplane can vary greatly depending on factors such as the type of aircraft, weather conditions, and flight path. However, the average cruising speed for a commercial jet is around 550 miles per hour.

How is the speed of an aeroplane measured?

The speed of an aeroplane is typically measured using an airspeed indicator which calculates the difference between the pressure of the air entering the aircraft and the surrounding atmospheric pressure. This is then converted into a speed measurement in knots or miles per hour.

Can the speed of an aeroplane change during flight?

Yes, the speed of an aeroplane can change during flight. Pilots have the ability to adjust the throttle and change the speed of the aircraft as needed. Additionally, external factors such as wind can also impact the speed of the aeroplane.

How do pilots calculate the speed of an aeroplane?

Pilots use a combination of instruments and calculations to determine the speed of an aeroplane. They take into account factors such as air pressure, temperature, and altitude to accurately calculate the speed.

Can the speed of an aeroplane exceed the speed of sound?

Yes, some military and experimental aircraft have the ability to exceed the speed of sound, also known as supersonic speed. However, most commercial aircraft are not designed to fly at these speeds and are limited to subsonic speeds.

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