Arescue 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-third its altitude above the ocean. (a) if it takes the sound 1.92 s to reach the plane, determine the speed of the plane. (take the speed of sound to be 343 m/s.) /s (b) what is its altitude?

a) Speed of the plane= 108.47 (m/s)

b) Altitude of the plane: 624.77m

Explanation:

Using the speed of sound and the time it took to get to the plane we can determine the distance the sound traveled:

d=(343m/s) × (1.92s) = 658.56m

From the Pythagorean theorem, taking as the altitude and distance traveled two legs of a triangle and the situation traveled by the sound to the plane as the hypotenuse of this, we can establish the following equation:

(658.56m)²=( (1/3)×h)² + h²

Being h the altitude of the plane.

From here we can clear the altitude of the plane:

433701.27m² = (10/9)×h²

h²= 433701.27m² × (9/10)

h= (390331.14m²) ^ (1/2)

h= 624.77m

We know that the distance traveled by the plane until the sound is received is one third of the altitude, so this distance will be:

Distance= (1/3) × 624.77m= 208.25m

Considering the time in which the plane traveled this distance we can know the speed of it:

V= (208.25m) / (1.92s) = 108.47 (m/s)

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards