Baseball physics question?

Question

Can anybody figure out how many times harder you would have to hit a 12'' softball to travel the same distance as a 9" baseball. All conditions, wind, humidity, altitude, and temperature are the same.

Lets say it's off a tee, or the ball is pitched at the same speed from the same distance.

Answer 1

Let ball 1=9'' ball, ball 2=12'' ball, m1=mass of ball 1, m2= mass of ball 2, d1=density of ball 1, d2= density of ball2, v1= volume of ball 1, v2= volume of ball 2, D= diameter of ball 1, D2= diameter of ball2, S= distance balls travel, V= initial velocity of balls (they must be equal),F1= force required to hit ball 1 and F2= force required to hit ball 2. We know that d1=d2=d. Then:
m1=d*v1---(1)
m2=d*v2----(2)
Working on (1) and (2), we get
m2=m1*v2/v1=m1*(D2/D1)^3----(3)
Using energy formula,
F1*S=0.5*m1*V^2
F1=0.5*m1*V^2/S---(4)
F2=0.5*m2*V^2/S---(5)
Writing (4) and (5) in terms of m1 and m2, respectively we get:
m1=2*S*F1/V^2---(6)
m2=2*S*F2/V^2---(7)
Inserting (3) into (7) and equating the result to (6), we get:
F2=(D2/D1)^3*F1
F2=(12/9)^3*F1
F2=1.1F1
Therefore, you have to hit ball 2 roughly 10% harder than ball 1. Generally for such cases the force required is the known force multiplied by the cube of the ratio of the diameter of new ball to diameter of the given ball.

Answer 2

It depends on how fast the pitch is traveling when you hit it. If it is traveling fast (90mph) then the batter doesn't have to generate a lot of power. The pitcher does most of the work. If we're playing slow pitch softball, the batter will have to generate ALL of the power.

Answer 3

Show us your reasoning and your work so far and we'll be willing to help you.