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

=(h^{2}+h^{2}/16)^{1/2} [pythagoras
theorem]

=(17h^{2}/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)

4. An air plane flies horizontally with
X-velocity V0x= 360 m/s at
an altitude (height above the ground)=H=Dy= 3645
m. A bag of mass M=40 Kg falls off from
the plane, and moves to the ground in a parabolic path without air
resistance while the plane ciontinues to fly horizontally. Use
g=10 m/s2 and V0Y=0
Part A
The time the bag takes to hit the ground is t=____
seconds
The time the bag takes to hit the ground is t=____...

1.You are in a plane that flies horizontally
with speed 900 km/h ( 250 m/s) when an engine falls off. Neglecting
air drag, assume it takes 25 seconds for the engine to hit the
ground.
(a) How high was the plane flying?
(b) What is the horizontal distance that the
engine covers before hitting the ground?
(c) If the plane somehow continuous to fly as
if nothing had happened, where is the engine relative to the
airplane...

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