How Do Kinematics Apply to a Fielder Catching a Ball?

[Harminder_Saini]

Homework Statement

You are enjoying some downtime watching a baseball game with a friend. In the bottom of the ninth inning, the ball is hit into the air at some initial velocity, a fielder at some initial position runs at a constant velocity and makes a spectacular catch. “That’s impossible! How did he catch that?” your friend says. Realizing that you have an opportunity to make an exciting event even more memorable, you take time to break down the play. You want to show your friend that the play was amazing, but not impossible (it did happen, after all) because the fielder had more than enough time to watch the ball and judge where it would land before running to make the catch. Assuming that the fielder ran directly to the spot where the ball was caught and caught the ball at the same vertical height that it was launched from, what was the fielder’s reaction time?

Relevant Equations

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I don't know how to approach this question. This question is on my Midterm tomorrow and the teacher gave it to us without the values in order for us to get an understanding help

 

[collinsmark]

The teacher gave you the problem without any values. That's fine, just keep things in terms of variables.

So your first order of business is to start defining some variables. Start with things like the ball's initial velocity, the angle above the horizontal of the ball's initial trajectory, speed of the fielder, etc. (there's one or two more variables that you'll want to define.)

Then go from there.

 

[Harminder_Saini]

Yes, I have done this but I don't understand what the question means by "what is the fielder's reaction time". How would I find the reaction time?

 

[collinsmark]

Yes, I have done this but I don't understand what the question means by "what is the fielder's reaction time". How would I find the reaction time?

I would say that his "reaction time" is whatever time he has left: The amount of time that the ball is in the air minus the amount of time that the fielder is running.

 

[Harminder_Saini]

So I would use Velocity/Gravity which will give me the maximum height. Then I multiply by 2 to see how long it takes for the full throw. Then I would rearrange V=d/t to find the d then subtract that from the position of the fielder when I find the displacement of the fielder I can use his initial velocity and displacement plug it into v=d/t and rearrange to find t and finally subtract the time of the fielder and the ball to find the reaction time.

 

[collinsmark]

So I would use Velocity/Gravity which will give me the maximum height.

I hope you don't mean velocity divided by the acceleration due to gravity (that won't work). But you could use one of your kinematics equations to calculate the maximum height if you wanted to.

But you really don't even need to calculate the maximum height. There is a to determine the ball's air time more directly.

Then I multiply by 2 to see how long it takes for the full throw.

Again, there is a way to determine the ball's air time more directly.

Then I would rearrange V=d/t to find the d then subtract that from the position of the fielder when I find the displacement of the fielder I can use his initial velocity and displacement plug it into v=d/t and rearrange to find t and finally subtract the time of the fielder and the ball to find the reaction time.

The rest sounds about right (I think). Again, though, this comes down to clearly defining your variables. Don't use the same variable $t$ for the ball's air time, the fielder's running time, and the reaction time. Use different subscripts or something on each of them to avoid confusion.

The same goes for the velocity $v$. There's the ball's initial vertical component of velocity, the ball's initial horizontal component of velocity, and the fielder's velocity.