How Long Until the Bomb Hits the Ground?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]. 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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