# A Spectacular RAAF Roulette Air Show!

• 53Mark53
In summary: You are asked to find how fast the angle of vision is changing(w.r.t.ground, since height of the person is neglected). Form an equation which relates this angle to the given quantities. That's where trigonometry comes into picture. Start with a diagram. It will make a lot of things clear for you.In summary, when the aeroplane is x=180metres horizontally from a person looking North, their head will rotate up to h=340metres in radians per second.
53Mark53

## Homework Statement

An RAAF Roulette aeroplane is performing a low fly over at an air show. Under the current wind conditions its top speed is 450 km/hour, and it will fly directly over the crowd at an altitude of only h=340metres approaching from the North. When the aeroplane is only x=180metres horizontally from a person in the crowd looking North, how fast are they rotating their head upwards to keep the aeroplane in the centre of their vision?

You should neglect the height of the person in your calculations. Give your answer in radians per second, either exactly or correct to three decimal places.

## Homework Equations

would I need to use pythagoras to solve this?
Does this mean that dx/dt is 450?

Any help would be much appreciated

53Mark53 said:
would I need to use pythagoras to solve this?
Does this mean that dx/dt is 450?
You will need to use trig and calculus. I would recommend working ent irely algebraically (no numbers!) until the final step, and don't forget to convert to standard units.

haruspex said:
You will need to use trig and calculus. I would recommend working ent irely algebraically (no numbers!) until the final step, and don't forget to convert to standard units.

does this mean:

s^2=h^2+x^2

differentiating

2s=2h+2x

s=h+x

what would I so now?

You are asked to find how fast the angle of vision is changing(w.r.t.ground, since height of the person is neglected). Form an equation which relates this angle to the given quantities. That's where trigonometry comes into picture. Start with a diagram. It will make a lot of things clear for you.

Last edited:
53Mark53 said:
does this mean:

s^2=h^2+x^2

differentiating

2s=2h+2x
No, this makes no sense. From ##s^2## to 2s, you are apparently differentiating with respect to s, but from ##h^2## to 2h, you're differentiating with respect to h. You are also differentiating ##x^2## with respect to x.

In other words, ##\frac{d s^2}{ds} = 2s## and ##\frac{d h^2}{dh} = 2h##. If you differentiate both sides of an equation, the differentiation must be done with the same variable.

What you're missing is that s, h, and t are all functions of t.
53Mark53 said:
s=h+x

what would I so now?

## 1. What is a RAAF Roulette Air Show?

A RAAF Roulette Air Show is a high-energy aerial performance put on by the Royal Australian Air Force's aerobatic display team, the Roulettes. The team consists of seven skilled pilots who perform a series of thrilling maneuvers and formations in their PC-9/A aircraft.

## 2. Where can I see the RAAF Roulette Air Show?

The RAAF Roulette Air Show is performed at various air shows and events across Australia. It is also regularly featured at major events such as the Australian Grand Prix and the Royal Edinburgh Military Tattoo. Check the official RAAF website or local event listings for upcoming shows.

## 3. How long does the RAAF Roulette Air Show last?

The length of the RAAF Roulette Air Show can vary depending on the event and the weather conditions. On average, the show typically lasts between 20-30 minutes. However, the team is known for being flexible and can adjust the length of the show to fit the event schedule.

## 4. Is the RAAF Roulette Air Show safe?

Yes, the RAAF Roulette Air Show is carefully planned and executed with safety as the top priority. The pilots undergo extensive training and follow strict safety protocols during the show. The aircraft used are also regularly maintained and inspected to ensure their safety and reliability.

## 5. Can I meet the pilots after the RAAF Roulette Air Show?

Yes, the pilots are often available to meet and greet with the audience after the show. This is a great opportunity to ask questions and learn more about the RAAF Roulette team and their impressive skills. However, please note that this may not be possible at all events and is subject to the team's availability and schedule.

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