# Homework 6 Problem 6

Monday, March 14th, 2016

6.         Consider Willie Mays hitting a homerun.  Model the ball as particle and consider the motion of the particle (ball) in two dimensions (the ball moves in a vertical plane).

6a.       Draw a FBD of the ball immediately after impact from the bat

6b.       Write out the governing equations of motion for the ball

6c.       Determine the minimum initial velocity required to clear the wall by 1 foot for each park

6d.       Consider the effect of Wind resistance at each park.  Write out the governing equations of motion for the ball including the Drag Force.

6e.       Derive the differential equations for the velocity of the ball in the E1 and E2 directions at any time t.  Do not solve the equations.

## 354 thoughts on “Homework 6 Problem 6”

1. Myra Fabro says:

Just curious how people left their answers for 6d and 6e.

Did anyone leave their answers with just the variables or did you plug in the given constant values into the equation?

2. Erik Hansen says:

Anyone else get a tough equation to take the integral of?

3. Daniel Joseph Conway says:

I’m a little confused on when we apply drag force. The way I read the problem makes me think that we are using drag on all parts of the problem but only taking wind into account on part D and E. Is that right, or is there supposed to be no drag force on A B and C?

1. Ryan Asher says:

I was assuming that drag force and wind resistance are different factors. I am using drag force for all parts and using wind speed as an input to the velocity used in the drag force equation for parts d and e. Where total velocity is velocity of the ball plus wind speed.

4. Herberto Dutra says:

On parts a, b and c the problem states that the wind resistance needs to be neglected. The only acting force on a, b and c is the weight. The speed in the E1 direction is constant

5. Erik Hansen says:

I should clarify: I am referring to parts 6d and 6e.

6. Alison Ling says:

For part c, I tried work-energy equation but how do we determine the ball’s velocity at the given distance? If we assume constant velocity, then I am getting a pretty small value for velocity which doesn’t seem right.

1. Herberto Dutra says:

I solved c) by using kinematics only . I used S = So + VoT in the horizontal direction to get a formula for time and substituted this time expression in the vertical component. Then I substituted the values for each stadium. I found really reasonable values. Anybody did it differently ?

7. Erik Hansen says:

I started with sum of forces equation and solved for acceleration, then took the integral with respect to time. It really pushed my integral skills and knowledge of the various rules.

1. Myra Fabro says:

You shouldn’t need to take the integral. If you’re referring to part e, you are to just derive the differential equations and don’t need to solve by integration.

8. Thomas Wayne Butts says:

So I’m assuming the wind velocity comes into play in the drag force equation, making v more of a relative velocity (velocity of the ball and wind). Does that sound right? Is that the only place this relative velocity would be used?

1. Ryan Asher says:

After reading the problem multiple times, that is the conclusion I have come to as well.

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