# Determine Speed of Plane Flying Horizontally

• reza1
In summary, the problem involves finding the speed of a plane that passes overhead at a height h and causes a sonic boom at a specific time t1. Using the right triangle formed by the height, speed of sound, and time, the speed of the plane can be calculated using the Pythagorean theorem.
reza1

## Homework Statement

A plane traveling horizontally passes overhead at a height h at t=0. at time t=t1 a sonic boom i heard.

b.) Determine the speed of the Plane

Ma=1/sin(pheta)
pheta=arctan(h/x)

Ma=1/sin(arctan h/vt)

I think I've done it correct up to this point...
Do i have to find the sin of (arctan h/vt) which is h/vt/ SQRT(h^2-vt^2)... ? i don't know how to solve for V ... any help would be appreciated thank you

## The Attempt at a Solution

You really don't need any angles. Draw the right triangle at time t1. The two sides are h and v*t1. If c is the speed of sound then the hypotenuse is c*t1. Use the pythagorean theorem and solve for v1. The problem is simpler than you think.

## 1. How is the speed of a plane flying horizontally determined?

The speed of a plane flying horizontally can be determined by using a variety of methods, such as radar, GPS tracking, or airspeed indicators. However, the most accurate and commonly used method is by using a pitot tube, which measures the difference between the static and dynamic air pressure to calculate the speed of the plane.

## 2. What factors can affect the speed of a plane flying horizontally?

The speed of a plane flying horizontally can be affected by various factors, including wind speed and direction, air density, temperature, and the weight and aerodynamics of the plane itself. These factors can either increase or decrease the speed of the plane, and must be taken into consideration when determining its speed.

## 3. Can a plane fly faster than the speed of sound when flying horizontally?

Yes, it is possible for a plane to fly faster than the speed of sound when flying horizontally. This is known as supersonic flight and requires specialized aircraft and technology. However, it is not a common practice due to the high energy and technical requirements.

## 4. How do scientists measure the speed of a plane flying horizontally?

Scientists use various tools and techniques to measure the speed of a plane flying horizontally. These include radar, GPS, airspeed indicators, and flight data recorders. Advanced technologies such as laser doppler velocimetry are also used to measure the speed of planes with high precision.

## 5. Does the speed of a plane flying horizontally affect its fuel consumption?

Yes, the speed of a plane flying horizontally can affect its fuel consumption. As the speed of the plane increases, the drag and resistance also increase, requiring more fuel to maintain the same speed. Therefore, flying at a higher speed can result in higher fuel consumption, while flying at a lower speed can help conserve fuel.

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