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 receives the horn's sound, the plane has traveled a distance equal to one-fourth its altitude above the ocean. Assuming it takes the sound 2.16 s to reach the plane, and taking the speed of sound to be 343 m/s, determine the following.

(a) the speed of the plane m/s

(b) the altitude of the plane m

Answer 1

Let the altitude of the plane be h meters

So,distance traveled by the plane before sound reaches it=h/4 meters.

Since ,initially,plane was just above the boat,total distance traveled by sound to reach the plane

=(h²+h²/16)^1/2 [pythagoras theorem]

=(17h²/16)^1/2=17^1/2 h/4 meters.

Speed of sound=343 m/s

Time taken for sound to reach the plane=2.16 s

So,distance=speed*time=>17^1/2 h/4 =343*2.16=>h=343*2.16*4/17^1/2=718.76 m

So,altitude of the plane=718.76 m .............................answer for (b)

Also,in time t=2.16 sec, plane travels a distance of h/4 meters=718.76/4=179.69 m

So,speed of plane=distance/time=179.69/2.16=83.19 m/s...........................answer for part (a)