A cargo plane is flying horizontally at an altitude of 15km with a constant speed of 835km/hr when a large crate slides out of the rear of the plane.A cargo plane is flying horizontally at an...

A cargo plane is flying horizontally at an altitude of 15km with a constant speed of 835km/hr when a large crate slides out of the rear of the plane.

A cargo plane is flying horizontally at an altitude of 15km with a constant speed of 835km/hr when a large crate slides out of the rear of the plane. The acceleration of gravity is 9.81m/s^2. How far is the crate from the aircraft when the crate hits the ground, assuming that the plane continues to fly with constant velocity? Answer in units of km.

Asked on by pavilion77

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txmedteach's profile pic

txmedteach | High School Teacher | (Level 3) Associate Educator

Posted on

So to answer this question, you'll need to recall some things about ballistic trajectories. First, we're going to assume there is no air resistance. Therefore, there is no air slowing the box down.

Because air resistance is not slowing the box down, it will actually be travelling the speed of the plane in the horizontal direction as it falls!

If you want to think of it in terms of vectors, the horizontal component of the velocity will remain constant, while the vertical component will start at 0, and increase at a rate of 9.8 m/s^2.

BUT WAIT! The vertical distance does increase as the box falls, but the horizontal distance doesn't! Based on our vectors, if you're in the plane, you would just see the box drop just like if you dropped a penny off of a skyscraper!

So, we got lucky here! We don't really even need to do any calculations!

Because the plane is flying at an altitute of 15 km, and because the box has no horizontal velocity difference from the plane, the box will be 15 km from the plane (only difference in vertical direction) when it hits the ground.

I hope that helps!

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najm1947's profile pic

najm1947 | Elementary School Teacher | (Level 1) Valedictorian

Posted on

When an aeroplane is moving with a certain speed in the horizontal direction, everything inside it is also moving with the same speed and in the same direction. If anything slides out or drops from the plane, then it is pulled towards the ground with an acceleration equal to g (8.81m/s^2) but at the point of exit, its speed in the horizontal direction remains equal to the speed of plane.

If the air resistance is not considered, then in that case the crate sliding down will cover the same distance horizontally as covered by the plane and at the time of hitting the ground, the distance between the cargo plane and the crate will remain 15 km.

However if the crate is subjected to the air resistance, which is bound to be there due to its large size, both the vertical and horizontal speed will affeted depending on the magnitude of the air resistance.

As the value of air resistance is not provided in the question, the problem cannot be solved to find a numerical value of distance between the cargo plane and the crate in Km.

 

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