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### How Long Until the Bomb Hits the Ground?

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Date: 8/25/96 at 13:42:16
From: Anonymous
Subject: Plane Drops Bomb....

A bomber flying at 32,000 feet over level terrain drops a 500-pound
bomb.

a. How long will it take the bomb to strike the ground?
Using the position equations s = -16t^2 +vt + s
I got an answer of 44.721 seconds before impact.

My first question is, how does the weight of the falling object factor
into the velocity at which it is falling, since it is reasonable to
assume an object of a heavier mass would fall at faster rate.

b. If the plane is flying at 600 mph how far will the bomb travel
horizontally during its descent?

This is the part of the problem that is giving the most concern.
If the bomb is being dropped out of the plane, would not the force of
gravity and the tendency for the bomb to fall be greater than the
velocity of the plane carrying it, therefore causing it to fall
straight down? However, it could also be reasoned that if it takes
44.721 seconds for the bomb to hit the ground then it is falling at
approximatlely 715.54 ft per second. So during the first second would
it still be travelling with the velocity of the plane and would have
travelled 10 miles in the first second [600mph/60sec].
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Date: 8/25/96 at 15:25:5
From: Doctor Robert
Subject: Re: Plane Drops Bomb...

In the absence of air resistance (which is only really valid outside
the atmosphere) all bodies accelerate at the same rate when falling in
the earth's gravitational field.  The reason for this is that the
FORCE that the earth exerts on a mass is proportional to that object's
mass, while the acceleration that the object experiences is inversely
proportional to its mass, so that the mass of the object cancels out.
So, in the absence of air resistance, a feather and a ton of bricks
accelerate at the same rate!

Your value of 44.7 seconds for the time of fall is correct.

When the bomb was dropped from the plane, it (the bomb) was traveling
at 600 mph.  Again, if we neglect air resistance, we can say that the
bomb was traveling at 600 miles per HOUR for 44.7 seconds.  How far
did it travel?

D = rate times time = 600 miles/hour times 44.7/3600 hours

which is approximately = to 7.45 miles.

I hope that this helps.

-Doctor Robert,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
High School Physics/Chemistry

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