Hyperbola - Find focus, equations of asymptotes, etc.

May 19th, 2015
Price: $5 USD

Question description

When a fighter jet travels faster than sound, it generates a sonic boom shock wave in the shape of a cone. If the plane is flying at a constant altitude, this cone intersects the ground in the shape of one branch of a hyperbola. Suppose a jet is flying north at level altitude and at a speed of 500 m/s (which is a supersonic speed). In this model, let the position of the jet be the origin. The vertex of the sonic boom hyperbola is on the ground 15 km behind the jet, and the hyperbola has an eccentricity of 1.5. Use a scale of 1 unit = 1 km for this model. Answer the following:

I) Find the coordinates of the focus and the equations of the asymptotes. Round all answers to the nearest hundredth. 

II) Write an equation for the sonic boom hyperbola in standard form.

III) A person on the ground will hear the sonic boom when the hyperbola passes over him. Suppose the jet is located at the otigin at time t = 0. The jet and the sonic boom line are moving due north at 500 m/s, and John is standing at (7,10). Calculate the time, in seconds, until John will hear the sonic boom. Round the answer to the nearest tenth of a second. 

Tutor Answer

(Top Tutor) Daniel C.
School: UIUC

Studypool has helped 1,244,100 students

Review from our student for this Answer

May 19th, 2015
"Top quality work from this guy! I'll be back!"
Ask your homework questions. Receive quality answers!

Type your question here (or upload an image)

1823 tutors are online

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors