Question

when a figher 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 vertix of the sonic boom hyperbola is on the ground 15km behind the jet, and the hyperbola has an eccentricity of 1.5 use a scale factorof1unit = 1km for this model.

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 the time t=0. the jet and the sonic boom line are moving due north at 500m/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.

please show the steps of how to get the answer.

Answer 1

Cauhen a gene rales +he shape 6gher jet osier than Sonic boom shock waue in ound ft S C T the plane is his cone a cone eonstant altitude intersècts the fround in the shape o braneh og hyрезьаlа. One To calculate The dime in the second until John the sonic boom. uiu hear now, Caie hawe to ind distance between the hyperbala and Tohn at (7, 10) 2 2 8 24 put x:7 in eqO, we qet 2. 2 2 S 281 24 2 2S 4 9 2 8 1.24 2 25 2 281.24 2 2 S

1.174 Y 2 2 26G.15 6.25 duis tanceLo-6.25) 26.25 km 262 50 m Speed 26 2S0 speed o o S t S2.5 sec