1D Kinematics Legacy Problem #23 Guided Solution

A good problem solver will take the time to carefully read the problem and get a picture of what's going on. It will take the time to actually extract numerical information and equate it with variables within physics equations. It will take the time to plot a strategy as to how to get from the given information to the unknown information. Here we'll practice those habits and it begins with a star baseball player who's sliding into third base, hits the ground and has a velocity of 6.75 meters per second, slides across the dirt, reaches the base, still moving at 5.91 meters per second, all the way the player's accelerating with a negative acceleration indicating the slowing down. What we wish to find is the distance the player slides along the ground, which you wouldn't expect to be very far, but you'd expect it to be a reasonable one, two meters, something like that. So the way I'm going to do this is I'm going to take that 6.75 meters per second and I'm going to equate that with V0. I'm just going to write down V0 equals 6.75, then I'm going to write down Vf equals 5.91. That's the original and the final velocity at the beginning and the end of this acceleration period. Then I'm going to write A equals negative 5.11, and if the negative bothers you it simply means that we're slowing down. And finally I'm going to write D equals question mark. I've identified my known variables and my unknown variables and I'm going to plot a strategy. That strategy centers around finding an effective equation for solving for my unknown using my known values. And in this unit we have the big four. And the big four are the kinematic equations. Each have within them four variables. If you know any three of the four, you can calculate the fourth. The equation I'm looking at is going to have in it V0, Vf, A, and D. And it's the equation that goes Vf squared equals V0 squared plus 2A D. And in that equation I know everything but D. So I'm going to plug my numbers in. I'm going to go 5.91 squared equals 6.75 squared plus 2 times negative 5.11 times D. I'm going to solve for D and I'm going to take my time. First calculate what the squared terms are and then I'm going to subtract the 6.75 squared from both sides of the equation to get the D term by itself. And then once I've done that, I'm going to evaluate the left side. 5.91 squared minus 6.75 squared. Find out what that is. Then I'm going to divide by 2 and divide by negative 5.11. That will give me my answer. It should be a positive number and it should be about 1.04 meters.