How is the acceleration of a car traveling on an elevated air track related to the angle of elevation and the height of elevation?

Elevation reduces the speed of the car due to increasing gravitational pull and difficulty in movement.

The acceleration of a car traveling on an elevated air track is directly related to the angle and height of elevation because elevation changes the speed of the car due to gravitational pull.

When there is lower angle and height of elevation then less reduction occurs in the speed of car and vice versa so we can conclude that acceleration is directly related to the angle and height of elevation.

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on a given inclined we know that net force is given by

here we know that

so here we have

so here acceleration depends directly on angle of inclination

now we also know that if height of the inclined is H and its length is L

then we can write

so the acceleration is given as

so acceleration also depends directly on height of the inclined plane

1413.7 mi/h

Explanation:

height in air (H) = 30,000 ft = 30,000 x 0.3048 = 9,144 m

speed in air (v) = 550 mi/h = 550 x 0.44704 = 245.872 m/s

mass of aircraft = 255,000 lb = 255,000 x 0.453592 = 115666.054 kg

magnitude of the work done by drag force (W) =  2.96 × 10^6 Btu = 2.96 × 10^6 x 1055.06 = 3,122,977,600 J

acceleration due to gravity (g) = 32.08 ft/s^{2} = 32.08 x 0.3048 = 9.8 m/s^{2}

Take note that all values above are converted to their   standard units

kinetic energy in air (KE1)=   0.5m = 0.5 x 115,666.054 x = 3,496,182,316.8 J

potential energy in air (PE1) = mgh = 115,666.054 x 9.8 x 9,144 = 10,364,973,898.2 J

potential energy on the ground (PE2) = 0 since height (h) is 0

from the energy balance equation KE2 + PE2 = KE1 + PE1 - W

where KE2 = kinetic energy on the ground and PE2 = 0

we now have KE2 = KE1 + PE1 - W

substituting all values into the equation above we have

KE2 = 3,496,182,316.8 + 10,364,973,898.2 - 3,122,977,600

KE2 = 10738178615 J

recall that kinetic energy = 0.5m , hence

10738178615 = 0.5 x 115666.054

 = = 185675.5

v=

v = 430.9 m/s = 430.9 x 3.28084 = 1413.7 mi/h