When an airplane travels Taster than the speed of sound, the sound waves torm a cone behind the airplane. when the airplane is flying parallel to the ground, the sound waves intersect the ground in a hyperbola with the airplane directly above its center. A sonic boom can be heard along the hyperbola. You hear a sonic boom that is audible along a hyperbola with the equation x 2 100 − y 2 4 = 1herex and y are measured in miles. What is the shortest horizontal distance yoU could be from the airplane?

Question

When an airplane travels Taster than the speed of sound, the sound waves torm a cone behind the airplane. when the airplane is flying parallel to the ground, the sound waves intersect the ground in a hyperbola with the airplane directly above its center. A sonic boom can be heard along the hyperbola. You hear a sonic boom that is audible along a hyperbola with the equation            x              2              100    −            y              2              4    =  1herex and y are measured in miles. What is the shortest horizontal distance yoU could be from the airplane?

Jaiden Gould · Accepted Answer

x              2              100    −            y              2              4    =  1 is of the form             x              2                    a              2              −            y              2                    b              2              =  1 so it is a horizontal parabola with a center at the origin and vertices of   (  ±  a  ,  0  )The shortest horizontal distance you could be from the plane is the distance between the center and vertex of the hyperbola.Since       a          2        =  100, then a=10. The distance between the center and vertex of the hyperbola is then a = 10 so the shortest distance you could be from the airplane is 10 miles.Result:10 miles

Answered question

Answer & Explanation

New Questions in Wave motion