1D Kinematics Legacy Problem #27 Guided Solution

Physics problems typically begin as word problems and the end as mathematical exercises. And it's in the in the between, the time between the reading of the problem and the actual use of the calculator to calculate the answer, that most of the work gets done. Here we read about a California condor that's approaching the nest. It approaches and makes an upward swoop, achieving a momentary upward, not a trivial word, upward velocity of 12.8 meters per second. When the carrion that is carrying it as a beak falls from its mouth and begins to fall and hits a cliff outcropping 32.1 meters below. So the focus is on this carrion, this dead meat, this crow found on a road or whatever it would be, that is falling through the ear. What we know about is it begins its fall with an upward velocity of 12.8 meters per second. So we would say BO equals 12.8 meters per second. And we know that it falls a distance of 32.1 meters and hits a rock below. So we know that D equals negative 32.1 meters and I have to supply that plus and minus sign carefully by reading the problem and visualizing what's going on. Now it's falling and I can kind of pick up on the idea that if something's falling on this unit, oftentimes it's a free falling motion. And so A equals negative 9.8 meters per second per second. What we're asked to calculate is the speed just before it hits this outcropping to find the VF value. And so what I know is VO is positive 12.8 meters per second, I know D is negative 32.1 meters, I know A equals negative 9.8 meters per second per second. And I'm looking for VF. So the key will be to look through, scan through your list of kinematic equations, find the one equation that has in it these four variables. And if you've written them down, and written them down not just as numbers but as VO equal and D equal and A equal, now you know what to look for. So there's only one such equation that has all four variables in it. It's the one that goes VF squared equal VO squared plus 2AD. Now I'm going to be real careful with my algebra here and substitute all the numbers that I have into the right side of that equation. It would become VF squared equal 12.8 squared plus 2 times negative 9.8 times negative 32.1 meters. Now I evaluate the whole right side and that's equal to VF squared. Take the square root of both sides and so VF is either a plus or a minus, a square root of whatever we have here. Now the question asks for the speed so the plus and minus values have to do with velocities. All you need to know is the numerical value, the magnitude, and that's the answer. And you got it.