Question

5. A jet aircraft is travelling at 850 km/hr at an altitude of 11 km – when an engine falls off! a. Neglecting air resistance, determine the speed of the engine when it hits the ground. Is this realistic? Discuss how assumptions made in the calculations might not reflect the reality of the engine's impact speed. What value might the impact speed actually be and why? b. Determine the horizontal range of the engine (measured from where the jet was located when the engine fell off). c. Reality – Would the engine land at this point in reality? Why or why not? Under what conditions would your solution be valid? Where (roughly) would it actually land?

Answer 1

Answer:

a. 851.65 km/hr

b. 353.56 m.

c. In reality, due to the effect of air resistance, the engine will hit the ground before the above range of 353.56 m

Explanation:

The parameters given are;

Speed of aircraft = 850 km/hr

Altitude of aircraft = 11 km

a. The equation of motion is given by the relationship;

Vertical velocity $v_y$;

$v_y$² = u² + 2·g·s

Where:

s = The height of the aircraft = 11 km

g = Acceleration due to gravity = 9.81 m/s²

u = Initial velocity = 0 m/s

$v_y$² = 0² + 2×9.81×11

$v_y$² = 215.82 m²/s²

$v_y$ = √(215.82 m²/s²) = 14.69 m/s

The horizontal velocity of the engine, vₓ, is given as 850 km/hr = 236.11 m/s

The resultant velocity $v_R$ = √($v_y$² + vₓ²)

$v_R$ = √(215.82 + 236.11²) = 236.57 m/s = 851.65 km/hr

The value is not realistic because there would be an effect on the motion of the engine due to air

The assumption of the absence of air resistance removes the slowing down effect of the air as the engine accelerates through the atmosphere when falling such that the real resultant engine impact speed is lesser than the calculated value based on the assumption of no air resistance

b. The horizontal range can be found from the relationship;

The range, R = vₓ × Time (t)

The time for the engine to reach the ground is given by $v_y$ = u + g·t

14.69 = 9.81 × t

t = 14.69/9.81 = 1.497 s

R = 236.11×1.497 = 353.56 m

c. In reality, due to the effect of air resistance, the engine will hit the ground before the above range of 353.56 m.

The solution will be valid where there is no effect of air resistance such as in a vacuum