1D Kinematics Legacy Problem #8 Guided Solution

Physics problems typically begin as word problems and end as mathematical exercises. And oftentimes those mathematical exercises are rather straightforward and easy, yet the problem is very, very difficult. This is an example of a problem whose mathematical operations are easy, yet the problem is rather difficult because of the conceptual nature of the problem. In order to hurdle this type of problem, what you need to do is read it carefully, picture and visualize the situation, start to think about what you know and what you're looking for, and then use good algebra skills in order to solve for the unknown. Now what we're told is we have a baseball that's moving one way, a batter hits it in the exact opposite, key word there, exact opposite direction. We're given the pre-collision speed of the ball and the post-collision speed of the ball, and we're also given the time that the ball and the batter are in contact, and it's during this time of .75 milliseconds that the ball undergoes this velocity change or acceleration. What we're asked to do is calculate the average acceleration. We know that to always be a velocity change divided by a time. So if we can just get a velocity change and get a time, and then pay attention to some units, we'll be able to get this problem correct. So how do you get the velocity change? Well, first you have to recognize that velocity is a vector and as such it has a direction. And before the collision with the bat, the ball's moving towards the batter, and afterwards it's moving away, and those are opposite directions. And typically the way we talk to our calculators in terms of directions is we use pluses and minuses. So you could say the ball's moving in the positive direction before the collision. If that's the case, after the collision it's moving in the negative direction. And always in science when you're calculating a change in a quantity, it's always the final minus the initial. So in this case it would be the negative 56 minus the negative 96. When you do that little mathematics, negative 56 minus negative 96, you get an answer that's bigger than the 96, and definitely it's not 40. And now that's the mile per hour delta V. Now you need to take that mile per hour delta V and divide it by a time. I notice times in milliseconds, you've got to give attention to that. You convert that to seconds by dividing it by 1,000. It's a really small time. You want to multiply by 1,000, that would give you 750 seconds, and you know a collision between bat and ball doesn't last that long. You have to divide by the 1,000 and you get your answer in time. You get your time in units of seconds, .00075 seconds. Now if you divide the delta V in miles per hour by the time in seconds, you're going to get your acceleration. And as you would expect, the smack of the bat on the ball, you'd expect it to be large, and it is. Now you've got it in miles per hour per second, they also ask you to calculate in meters per second per second. Fortunately, they give you a conversion factor. So one way to solve the problem is take the original delta V that you got in miles per hour, and then take that value, divide it by 2.24, and it gets you to meters per second. And then divide that by the time again. Or just simply take the miles per hour per second, and divide it by 2.24, and you get your acceleration in meters per second per second.