Projectile motion question (baseball problem)

[boomer77]

Homework Statement

The center of a baseball of diameter 8.20 cm is 1.320 m vertically above the plate when it is hit. The blast sends it off at an angle of 30.5° above the horizontal with an unknown initial speed. The outfield fence is 94.0 m away and 11.20 m tall: the ball just clears it. Ignoring aerodynamic effects, what was the initial speed of the baseball?

Homework Equations

-d=vt for the x direction
-any free fall equation for the y direction

The Attempt at a Solution

dx= 94.0m dy= 9.88m (subtracted the height in which the ball was hit at)
Vx= vcos(30.5 Viy=?
t= 94.0/vcos(30.5 a= -9.8m.s^2

d=vit+1/2at^2
9.88=vi(94.0/vcos(30.5)-4.9(94.0/vcos(30.5)^2
v^2(-99.22)= -58323.769
v^2= 5884.13
v=76.7m/s

where am i going wrong in this problem? help will be greatly appreciated, thanks!

 

[PhanthomJay]

You have Vx=vcostheta; how about Viy=vsintheta? Looks like you have missed that.

 

[boomer77]

thanks for the reply. do i add the diameter of the ball to when it clears the fence too? I'm pretty bad with word problems.

 

[PhanthomJay]

thanks for the reply. do i add the diameter of the ball to when it clears the fence too? I'm pretty bad with word problems.

i guess to be accurate to 2 places after the decimal point, you'd have to consider the ball diameter, that is, add half its diameter to the y height (y = 9.88 + 0.04 = 9.92) for what it may be worth.

 

[boomer77]

i'm still getting this problem wrong so my equation in the y direction would be

9.92=vsin(30.5(94/vcos(30.5)-4.9(94/vcos(30.5)^2

i come up with the answer of 3.88 m/s but my problem set says it's wrong

should i be doing something different?

 

[PhanthomJay]

i'm still getting this problem wrong so my equation in the y direction would be

9.92=vsin(30.5(94/vcos(30.5)-4.9(94/vcos(30.5)^2

i come up with the answer of 3.88 m/s but my problem set says it's wrong

should i be doing something different?

Looks like the correct approach; I'll check your numbers in a bit...I've got to pick up a take out order for the family..

 

[PhanthomJay]

i'm still getting this problem wrong so my equation in the y direction would be

9.92=vsin(30.5)[/color](94/vcos(30.5))[/color] - 4.9(94/vcos(30.5))[/color]^2

i come up with the answer of 3.88 m/s but my problem set says it's wrong

should i be doing something different?

Looks like a math error..I get V = 35.99m/s. Check your parentheses..check calculator set to degrees and not radians..

 

[boomer77]

thank you very much for the help!