1D Kinematics Legacy Problem #30 Guided Solution

NASA's Glenn Research Center in Ohio has a very, very tall tower known as a vacuum tower. And it's a tower that mostly is below the ground. And it's made of steel. It's large. And what they're able to do is use the tower to study free fall. They put objects inside of these metal boxes and they drop the boxes through the tower. And since there's very little air, if any at all, within the tower, they're able to study the effect of free fall accelerations upon things like fluids and flames and equipment that they're going to put up on vehicles going into space and things of that nature. Now, these little boxes that they drop are equipped with cameras, so they're able to kind of see what happens as the objects fall. Now, what we're told here is an object is going to free fall through this tower 132 meters. So the D is going to be negative 132 meters. The acceleration for free fall is negative 9.8 meters per second per second. And these objects are dropped from rest, so V0 is zero meters per second. We're asked to find two things, the time to fall when dropped from rest, and the final speed. So I'm going to do part A first where I'm looking to calculate a T. So like any of these problems in this set of problems, what I want to do is carefully write down what I know and express it in terms of the symbols that are found in the equation. So I have a D equal, I have an A equal, and I have a V0 equal, and I'm looking for T. So I need to find the one equation that's got all four of those symbols in it, and that equation is going to be the one that goes D equal V0T plus one-half AT squared. I'm going to try to solve for the T. My D is going to be plugged in as negative 132 meters. My V0 is zero, so the V0T term cancels. My right side becomes one-half times negative 9.8 times T squared. Be careful with your algebra. You're going to have to simplify the right side to negative 4.9 T squared, and then divide each side of the equation by negative 4.9. So the equation becomes negative 132 divided by negative 4.9 equals T squared. Evaluate the left side of the equation. That becomes positive. Take the square root of both sides, and you have your T. The second part of the problem involves finding the final speed just before it hits the ground. So you're looking for the equation that goes in it. The A, and the V0, and the D, and maybe even the T since you've now calculated that, and most importantly, the VF. So there's a couple of equations you could use. One of them is the equation that goes VF squared equal V0 squared plus 2AD. You have V0 is zero, and you have A, and you have D. And the other equation that you could use is the one that goes VF equal V0 plus AT since now you know the T from part A. So what you'll do is substitute values again into either one of those equations. Be careful with your algebra, and solve for the VF.