A supersonic jet airplane passing directly overhead creates a shock wave that makes an angle of 51∘
with the horizontal. What is the speed of the airplane?
I know that I need to use Sin(x)=c/v but keep getting an incorrect answer.
To solve this problem, you need to use the concept of trigonometry and the relationship between the speed of sound, the shock wave angle, and the speed of the airplane.
The formula you mentioned, sin(x) = c/v, is not the correct one for this problem. The formula you need to use is the sine formula for the velocity of an object in supersonic flight, which is given by:
sin(θ) = v/c
Where:
- θ is the angle the shock wave makes with the horizontal
- v is the speed of the airplane
- c is the speed of sound
In this case, you know that the shock wave makes an angle of 51° with the horizontal. Let's call this angle θ = 51°. The speed of sound, c, is typically around 343 meters per second (at sea level and room temperature).
Now, let's rearrange the formula to solve for the speed of the airplane, v:
sin(θ) = v/c
v = c * sin(θ)
Substituting the values into the formula:
v = 343 * sin(51°)
Using a calculator, evaluate sin(51°) to find the value, and then multiply it by 343 to get the speed of the airplane (v).
Once you compute the value, you'll have the speed of the airplane in meters per second. Remember to use consistent units when solving the problem.