Question

A plane flies at 1.75 times the speed of sound. Its sonic boom reaches a man on the ground 1.00 min after the plane passes directly overhead. What is the altitude of the plane? Assume the speed of sound to be 330 m/s.

Answer 1

you need to draw it,
A = the man position
B = where the jet pass overhead the man
C = position of the jet now, I put it on the right of B
D = source of the sonic boom which heard by the man at first time, it not from C but it would left of B

angle between AD and AC = 90 degree.
angle between AC and DC = ?
AD = v to ....... to = time need by sonic boom to be heard by man.
.............................it is time needed by sound wave move from D to A
DC = 1.25 v to
sin ? = AD / DC = 1/1.75 = 0.57
cos ? = 0.6
tan ? = 4/3

DB = 1.75 v * t1 = AB tan ? ; ......t1 = time needed by the jet to move from D to B
t1 = AB tan ? / 1.75 v ............................a)

t2 = 1 minute = 60 s .... t2 = on the problem
to = t1 + t2

AD = v to = AB /cos ?
v (t1 + t2) = AB /cos ?

subtitute ....a)
v t1 + v t2 = AB / cos ?
v (AB tan ? / 1.75 v) + v t2 = AB / cos ?
AB tan ? /1.75 + v t2 = AB / cos ?
AB * (1/cos ? - tan ?/1.75) = v t2

AB * (1/0.6 - (4/3) / 1.75 ) = 330 * 60
AB * 0.6 = 330 *60
AB = 30 000 m