Question

A 0.047 kg golf ball is driven from the tee with an initial speed of 54 m/s and rises to a height of 23.2 m.

What is its speed when it is 6.0 m below its highest point?

Answer 1

Do you even need to know the mass of the ball? I don't know, but I think that I need to determine the initial velocity in the y-direction, first:

Vf^2=Vi^2-2gd

where:

d=23.2m
Vf=0m/s
g=9.8m/s^2

Solve for Vi:

Vi=Sqrt(2*9.8m/s^2*23.2m)

Vi=21.32m/s

Conservation of energy tell me that

MEi=MEf

mgh+1/2mv^2=mgh+1/2mv^2

Masses are on both sides of my equation, so they cancel out.

gh+1/2v^2=gh=1/2v^2

Maybe I don't need to know the mass of the ball.

Solve for v:

where

For the left side of the equation

g=9.8m/s^2
h=0m
and
v=54m/s

For the right side of the equation

g=9.8m/s
h=23.2-6m=17.2m
and
v=??

Solve for the v:

0J+1/2(21.32m/s)^2=(9.8m/s)*(17.2m)+1/2v^2

227.32J=168.56J+1/2v^2

227.32J-168.56J=1/2v^2

Sqrt*[2*(1458J-168.56J)]=v

v=10.84m/s

Answer 2

For the left side of the equation

g=9.8m/s^2
h=0m
and
v=21.32m/s **** Correction

For the right side of the equation

g=9.8m/s
h=23.2-6m=17.2m
and
v=??

Solve for the v:

0J+1/2(21.32m/s)^2=(9.8m/s)*(17.2m)+1/2v^2

227.32J=168.56J+1/2v^2

227.32J-168.56J=1/2v^2

Sqrt*[2*(1458J-168.56J)]=v

v=10.84m/s

Answer 3

This is the whole thing corrected; ignore the previous two post.

Do you even need to know the mass of the ball? I don't know, but I think that I need to determine the initial velocity in the y-direction, first:

Vf^2=Vi^2-2gd

where:

d=23.2m
Vf=0m/s
g=9.8m/s^2

Solve for Vi:

Vi=Sqrt(2*9.8m/s^2*23.2m)

Vi=21.32m/s

Conservation of energy tells me that

Initial Mechanical Energy=Final Mechanical Energy

mgh+1/2mv^2=mgh+1/2mv^2

Masses are on both sides of my equation, so they cancel out, and I am left with the following:

gh+1/2v^2=gh +1/2v^2

I was correct: I don't need to know the mass of the ball.

Solve for v:

where

For the left side of the equation,

g=9.8m/s^2
h=0m
and
v=21.32m/s

And for the right side of the equation,

g=9.8m/s
h=23.2m-6m=17.2m
and
v=??

Solve for the v:

(9.8m/s^2)*(0m)+1/2(21.32m/s)^2=(9.8m/s)*(17.2m)+1/2v^2

0J + 227.32J=168.56J+1/2v^2

227.32J-168.56J=1/2v^2

Sqrt*[2*(1458J-168.56J)]=v

v=10.84m/s