How Far Does a Ball Fall Vertically in Projectile Motion?

[miamirulz29]

Projectile Motion and Level Horizontal Range.

Homework Statement

The acceleration of gravity is 32ft/s ^2.
If a pitch were thrown horizontally with a velocity of 96.9 mi/h, how far would the ball fall vertically by the time it reached home plate, 60ft away. Answer in units of ft.
So speed is 142.12 ft/s.

Homework Equations

Vx = Vxo + Axt
Y= Yo + VyoT + 1/2AyT^2 or Vy^2 = Vyo^2 + 2Ay(Y-Yo)

For the second equation, don't know which one to use.

The Attempt at a Solution

I got the time it took to reach 60 feet by using the first equation. T= 4.441. I don't know where to go from there. I think I use this equation: Y= Yo + VyoT + 1/2AyT^2

but I'm not sure. Any help would be appreciated greatly.

Edit: actually t= .422 seconds.

 

[miamirulz29]

Anybody?

 

[harvellt]

sorry

 

[miamirulz29]

I'm not sure what you are asking. Sorry to be such a pain.

 

[harvellt]

Sorry, ok so you know how long it takes for the ball to get from release to home. It travels a distance in the -y direction in that time. Thats what your looking for.

 

[miamirulz29]

using this equation: Y= Yo + VyoT + 1/2AyT^2, I got 57.151. That definitely is not right or is it?

 

[harvellt]

probably not what are you using for Vy at t=0? and if y=0 at the pitchers release what direction is acceleration in the y direction?

 

[miamirulz29]

I cannot figure out this problem. Maybe I got the time wrong. I don't even know what I'm looking for. Can somebody please clarify some stuff for me. I just want to know how to do it.

 

[miamirulz29]

probably not what are you using for Vy at t=0?

You mean Vyo, I used the original speed the ball was thrown, 142.12 feet/s. Is that wrong?

 

[harvellt]

yes that is wrong. That is the Vox, what is the Voy if the ball is thrown horizontally?

 

[miamirulz29]

zero?

 

[harvellt]

yep, and then what is the acceleration of the ball?

 

[miamirulz29]

OMG I just got it. Voy is 0! So it is -y = 1/2 (32) (.422)^2. Which gives me 2.849. Which is right in the computer. Thank you for your help!

 

[harvellt]

no prob!