Baseball Velocity and Components: Solving for Final Velocity and Height

[Tycho]

I'm not quite sure how to get started on this problem...

a baseball is struck by a bat, and 3 seconds later it is caught 30m away.

now the questions ask for it's final velocity, it's angle as it left the bat, the greatest height it reached, and the X and Y components of it's velocity as it was hit.
all of these things i can do if i had the speed of the ball initially. is it safe to assume that it is traveling at 10 m/s?

 

[Physics_wiz]

to find the X component of the initial velocity use v=d/t for the whole loop. To find the Y component of the initial velocity use V(final)-V(initial)=gt for half of the loop. I said half of the loop because you're looking at the velocity when the ball goes up in the air so that would take 1.5 seconds and on top the velocity is 0. After that, use vector addition to find the initial starting velocity and the angle.

 

[DivGradCurl]

I took a look at this website:

http://www.baseball-almanac.com/articles/fastest-pitcher-in-baseball.shtml

There is a list of the fastest pitchers in baseball. The speed range is 100-103 mph. So, let's consider a 100 mph pitch. We have

$$100 \frac{\mbox{miles}}{\mbox{hour}} \left( \frac{1,609.3 \mbox{ m}}{1 \mbox{ mile}} \right) \left( \frac{1 \mbox{ hour}}{3600 \mbox{ s}} \right) \approx 44.7 \frac{\mbox{m}}{\mbox{s}}$$

You're probably safe with $$v_i \leq 44.7 \frac{\mbox{m}}{\mbox{s}}$$.

A $$10 \frac{\mbox{m}}{\mbox{s}}$$ pitch is slow, but you can use it.

 

[NateTG]

I'm not quite sure how to get started on this problem...

a baseball is struck by a bat, and 3 seconds later it is caught 30m away.

now the questions ask for it's final velocity, it's angle as it left the bat, the greatest height it reached, and the X and Y components of it's velocity as it was hit.
all of these things i can do if i had the speed of the ball initially. is it safe to assume that it is traveling at 10 m/s?

If you take advantage of the fact that you know how long it flew, you should be able to determine the intial speed of the ball. In fact, since you're ignoring air resistance, it's the same as the final speed.

Perhaps you can figure out what the horizonal component of the ball's inital velocity.

P.S. Since the ball goes up and down during it's flight, it's traveling more than 30 meters. Since it's traveling more than 30 meters in 3 seconds, it's got to have started with a speed of more than 30 meters per second.