2D kinematics? Have equations but making errors?

[pinkerpikachu]

When Babe Ruth hit a homer over the 7.5-m-high right-field fence 95 m from home plate, roughly what was the minimum speed of the ball when it left the bat? Assume the ball was hit 1.0 m above the ground and its path initially made a 38º angle with the ground


2. Vx= Vcosθ x=horizontal distance, T=time, L=initial height h=final height
Vy= Vsinθ

x=vcosθT = x / vcosθ = T
h= L + vsinθT - (1/2)gT^2

The Attempt at a Solution

substituting for T

h= L + vsinθ(x / vcosθ) - (1/2)g(x / vcosθ)^2
h=L + xtanθ - (1/2)gx^2/ v^2 cosθ^2

v= sqrt[(L + xtanθ - (1/2)gx^2/cosθ^2) / h]

this should be how to get my answer which is 32, but I keep getting a number in the 90s. I actually get a negative under the sqaure root...but I ignore that...

 

[AvroArrow]

For this particular problem, x=95 m, h=7.5 m, L=1 m, θ= 38º, g=9.8 m/s² Putting these into the equation yields: v = sqrt[(1 + 95 tan38 - (1/2)(9.8)(95)^2/(cos38)^2) / 7.5] This gives a value of 36 m/s.

 

[thomate1]

I would suggest double-checking your calculations and making sure you are using the correct units for each variable. It's possible that a small error in one of the equations or units could lead to a significantly different answer. Additionally, it may be helpful to review the equations and make sure you are using the correct one for the given scenario. If you are still having trouble, I would recommend seeking assistance from a classmate or instructor to help identify and correct any errors.