1D Kinematics Legacy Problem #25 Guided Solution

As you learn to solve physics problems, it's important that you always carefully read the problem and make an effort to extract numerical information that's in the problem, either information that's explicitly stated or simply implied by small cues that are present within the problem. For instance, in this problem we're told an object's dropped from the top of a 71.3 meter tall tower and falls into some water below. We're told that it's dropped, and we're told also that it free falls to the water below. These two statements represent little implied hints about the motion of the object that first of all, since it's dropped and not thrown up or thrown down, we know that the original velocity, V0, is zero meters per second. We also know that it falls 71.3 meters. We could say D equals 71.3 meters. We could also say negative 71.3 meters, where the negative is the down displacement. And then finally, we're told it free falls, and what we know about free fall is we know that objects in free fall accelerate at a rate of 9.8 meters per second per second down. That would mean that we could say A equal negative 9.8 meter per second per second or simply 9.8 meter per second per second. What we're looking for is two things. First we're looking for the time to fall, and second we're looking for the speed at which it hits the water, a final speed. So the unknowns are T and Vf. So like any problem in this unit, we're looking for an equation that has the three known values and the one unknown value. Known values being V0, A, and D, and the unknowns being T and Vf. So I need to go through that list of kinematic equations that's provided on the overview page of this set of problems, and I need to find equations that do that. Now for the T equation, the one that works best is likely the one that says D equal V original T plus 1.5 AT squared. The term on the right side, V original T, actually cancels out since V original is 0. So the equation simplifies to D equal 1.5 AT squared. Take your negative 71.3 and put it in for D. Take your negative 9.8 and put it in for A. The right side becomes negative 4.9 T squared. Divide each side by negative 4.9 to get T by itself, then take the square root of each side and you have your answer for the T. To find your answer for the Vf, we have to return to our list of four equations and see if we can find one that has V0, T, and A and Vf in it. Indeed, there's one that goes Vf squared equals V0 squared plus 2AD. That's the equation of choice. And once more, the V0 squared term cancels out of that equation on the right side. So the equation becomes Vf squared equals 2AD. Your A is negative 9.8 and your D is negative 71.3. Plug those in, do some good algebra, and you end up with your answer.