How Does Linear Drag Affect a Baseball's Trajectory?

[SYoungblood]

Homework Statement

A baseball is hit at a height of 3 ft off thte ground. It leaves the bat with an initial speed of 165ft/sec, at an angle of 10 degrees from the horizontal. The linear drag coefficient is k=0.38; gravitational acceleration is 32 ft/sec^2

Homework Equations

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Find a vector form for the path of the baseball using these equations for linear drag,

x=V(sub)o/k (1- e^-kt) cos 10

y=(sub)o +V(sub)o/k (1- e^-kt) sin 10 + (g/k^2)(1- kt- e^-kt)

What is a vector form for the path of the baseball? Use only rational numbers in the expression as coefficients for the i and j vectors

The Attempt at a Solution

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Oh my, I am lost in the sauce on this one…

x=165/0.38(1 - e^-0.38t) *cos 10 = 427.61389 (1 - e^-0.38t)

y= 3 + 165/0.38(1 - e^-0.38t)*sin10 + 32/0.1444(1 + 0.38t - e^0.38t) = 3 + 81.8627(1 - e^-0.38t)+ 221.6066(1 + 0.38t - e^0.38t)

Well, I combined the constants, but how to get rid of the t variable in the equation is something that I simply am not seeing, any and all help is appreciated.

Once I get the vector equation, then my problem asks for things I assume are fairly standard for this type of equation, time in flight, range of the hit ball, does it clear the fence z feet away. That is all fairly straightforward, but have mercy, I have never seen this drag coefficient before and this is proving a tough starting block.

SY

 

[SteamKing]

The i and j position vectors (or x and y, if you prefer) are parametric equations in t. I don't think, given the nature of these equations, you can eliminate the parameter t. Besides, what purpose would elimination of the parameter serve in the solution of this problem anyway?

 

[SYoungblood]

The i and j position vectors (or x and y, if you prefer) are parametric equations in t. I don't think, given the nature of these equations, you can eliminate the parameter t. Besides, what purpose would elimination of the parameter serve in the solution of this problem anyway?

That was a thought that crossed my mind, and the only purpose I can see was that it answered the question on my homework. All the followup problems stem from it.

I think I will just write this off as a loss and drive on.

Thanks just the same,

SY