Supersonic plane flying horizontally

[olyviab]

Homework Statement

Dr.Botha sees a supersonic plane flying horizontally in a straight line, directly overhead. If the plane is flying at a height of 500m above the ground, and Dr.Botha hears a sonic boom 1.00s after the plane flies over him, where is the plane at the instant he hears the boom? Assume the speed of sound in the air is v = 343m/s.




2. The attempt at a solution
First attempt:
For the plane to produce a sonic boom, it must have been traveling at least at the speed of sound. So when the Dr. heard the sonic boom 1 sec after the plane flew over him, the plane must have traveled a distance of 343m in that one sec interval, therefore the plane is located 343m in the direction it was travel away from the doctor.

Second attempt:
Sin(theta) = (speed of sound / speed of plane)

theta = 46 therefore speed of plane = 471.4 and distance= 471.4m

 

[mgb_phys]

Not quite - how far is the person on the GROUND from the plane?

 

[willem2]

Moderator's note: this post moved from other deleted thread, where identical question was asked.

For the plane to produce a sonic boom, it must have been traveling at least at the speed of sound. So when the Dr. heard the sonic boom 1 sec after the plane flew over him, the plane must have traveled a distance of 343m in that one sec interval, therefore the plane is located 343m in the direction it was travel away from the doctor.

That won't do. It takes about 1.5 s for the sound to come to the Dr. The sound he hears 1s after the plane is overhead must have been emitted before the plane was overhead. There's nothing in the problem that says the plane can't go faster than the speed of sound.