A fighter jet is flying at Mach 3.2 in air of temperature 2 degrees C. What is the planes speed?
I really don't understand how to do this question. I'd appreciate your help!
the Mach number is how many times the speed of sound an object is moving
find the speed of sound based on the air temperature
So I tried this:
Mach # = v/sound
3.2 = v/332.22
1063m/s =v
Vsound = 331 + 0.61(2 degrees C)
=332.22
Would the 1063m/s be the correct answer?
To determine the plane's speed, we need to convert Mach number to the speed of sound in air. The formula to convert Mach number to speed is as follows:
Speed = Mach number × speed of sound
The speed of sound in air can be calculated using the formula:
Speed of sound = 331.4 + 0.6 × temperature
In this case, the air temperature is given as 2 degrees Celsius. Let's substitute this value into the formula and calculate the speed of sound:
Speed of sound = 331.4 + 0.6 × 2
= 331.4 + 1.2
= 332.6 meters per second
Now that we have the speed of sound, we can find the plane's speed by multiplying it with the Mach number:
Plane's speed = Mach number × speed of sound
= 3.2 × 332.6
≈ 1064.32 meters per second (rounded to two decimal places)
Therefore, the plane's speed is approximately 1064.32 meters per second.
To find the speed of the plane, we need to convert the given Mach number into units of speed. Mach number is a dimensionless quantity that represents the ratio of the speed of an object (in this case, the fighter jet) to the speed of sound in the same medium. The speed of sound varies with temperature, so we need to take that into account.
The formula to convert Mach number into speed is:
Speed = Mach number * Speed of sound
The speed of sound can be calculated using the following formula:
Speed of sound = 331.5 + 0.6 * temperature in Celsius
In this case, the temperature is given in degrees Celsius as 2 degrees C. So, by substituting this value into the formula, we get:
Speed of sound = 331.5 + 0.6 * 2 = 332.7 m/s
Now, let's calculate the speed of the plane:
Speed = Mach number * Speed of sound
Speed = 3.2 * 332.7
Speed = 1065.84 m/s
Therefore, the speed of the fighter jet flying at Mach 3.2 in air at a temperature of 2 degrees Celsius is approximately 1065.84 m/s.