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 the jet is flying north at a level altitude and at a speed of 500 m/s (which is supersonic speed) in this model let the position of the jet be the orgun the vertex of the sonic boom hyperbola is on the ground 15 km behind the jet and the hyperbola has a eccentricity of 1.5. Use a scale of 1 unit =1km for this model
·find the coordinates of the focus and the equations pf the asymptotes. Round all answers to the nearest hundredth.
·write an equarion for the sonic boom hyperbola in standard form
· a person on the ground will hear the sonic boom when the hyperbola passes over him. Suppose the jet is located at the origin at time t=0. The jet and sonic boom line are moving sue 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 your answer to the nearest tenth of a second.
