An airplane is flying horizontally with speed 1000km/h(280m/s) when an engine falls off. Neglecting air resistance, assume it takes 30s for the engine to hit the ground. (a) How highis the airplane? (b) How far horizontally does the engine travelwhile it falls? (c) if the airplane somehow continues to fly as ifnothing had happened, where is the engine relative to the airplaneat the moment the engine hits the ground??

a) h= 4410 m. b) 8400 m c) just below it.

Explanation:

a)

In the vertical direction, as the engine falls off, its initial velocity is 0. So, we can find the height from which it falls, applying the following kinematic equation for displacement:

       

Replacing g = 9.8 m/s², and t = 30 s, we can find h (in m) as follows:

       

So, the airplane is at a height of 4410 m when the engine falls off.

b)

Once released, as no other influence acts on the engine in the horizontal direction, it continues moving forward at the same speed that the airplane had at the moment that the engine starts to fall, i.e., 280 m/s.So, the horizontal displacement can be found just applying the definition of average velocity, as follows:

       

c)

If the airplane keeps flying horizontally at the same speed, it will be always over the engine, as both travel horizontally at the same speed. So, when the engine hits the ground, the airplane will be exactly over it, or the engine exactly below it.

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