1D Kinematics Legacy Problem #28 Guided Solution

You know, physics problems often begin as word problems and they end as mathematical exercises. And it's in the in-between time, between the time you read the word problem, and you actually begin to pick up your calculator and do the math, it's in the in-between time that the critical work is getting done. So here I'm going to read this problem. We're going to talk about the critical work. It says, Luke, Luke Apollo had reached a terminal speed of 10.4 meters per second as he approaches the ground with his parachute. During an attempt to snap one last photo with his camera, Luke fumbled it from a height of 52.1 meters above the ground. Of course it falls to the ground. We're asked two things about the camera. Determine the speed with which it hits the ground. Find the time for it to fall from Luke's hand to the ground when he's 52.1 meters above the ground. So that's the reading of the problem. Usually the next step is you want to go through and extract the numerical quantities. Find out what's what. And equate those numbers with actual variables that are found in your equation. So as I read, I see a 10.4 meters per second. And that's the original velocity of this camera before it begins to free fall. Now it's a downward velocity. I picked that up from the context of the problem. Luke is skydiving. He's falling down. So the camera's in Luke's hands. It's moving with Luke. And it's V0 is negative 10.4 meters per second. And it falls 52.1 meters to the ground. So that's the distance the camera's going to fall in this problem. And that's D equal negative 52.1 meters. And then finally, I can kind of presume that this camera's going to free fall. Since this is a unit we've been doing quite a bit of discussion on free fall. And so my A equal negative 9.8 meters per second per second. The free fall acceleration on Earth. Now I take the effort to write those numbers down and say they're equal to V0 and A and D. Now my unknowns are Vf and part A and T and part B. I'm going to do part A first. I want to find Vf. So now that I've identified known and unknown information, I'm going to plot a strategy. And the strategy here involves finding the equation that has within it the four variables you've identified. The three you know and the one you don't know. And so if I go back to the set's overview page, what I will find is that there's a list of four kinematic equations. I'm looking for the one that has V0, Vf, A, and D in it. And it reads something like this. Vf squared equals V0 squared plus 2Ad. Now I'm going to take my V0, my negative 10.4, and I'm going to put it in for V0 squared. I'm going to make sure I square it. And then I'm going to go plus 2 times negative 9.8 times negative 52.1. That whole term becomes positive by the time I go negative times negative. Then I'm going to add the first term, making sure I squared it. I'm going to add it to the second term. And then that's all equal to Vf squared. Take the square root of both sides and you have the Vf. And that's the first part of the problem. In the second part, you're going to kind of repeat the same thing looking for the T. Now there's a couple of ways to go about doing that because now you have another unknown. You have another known piece of information. You have the Vf value. So the way I like to solve this Part B is I like to use that Vf value. I like to use the equation that goes D equal V0 plus Vf over 2. That's the average velocity. V0 plus Vf over 2 multiplied by the time. Now I'm trying to solve for time in Part B. And I know the left side is negative 52.1. Over here on the right side, I'm going to put in the negative 10.4 plus my answer Part A, which is a negative value, divided by 2 times the T. And I'm going to solve for my T. And that's all there is to Part B.