sound phys qstn?

Question

A rescue plane flies horizontally at a constant speed, searching for a disabled boat. When the plane is directly above the boat, the boat's crew blows a loud horn. By the time the plane's sound detector perceives the horn's sound, the plane has traveled a distance equal to one-half its altitude above the ocean. Determine the plane's altitude.
A. 105 m
B. 652 m
C. 617 m
D. 422 m
E. 525 m

plz show me how u did it

Answer 1

Interesting problem. The distance the plane travels from the horn sounding until the sound detected is vt. This is 1/2 the altitude, so the altitude is 2vt. These form the legs of a right triangle. The hypotenuse is the distance the sound traveled, which is the speed of sound x t, so

(2vt)^2 + (vt)^2 = (vs*t)^2

5 v^2t^2 = vs^2t^2

v = 1/sqrt(5) * vs

Still need a constraint to get t. I guess I am not there yet.