What is the final velocity of the baseball after being hit by the bat?

[agadag]

Homework Statement

A pitcher throws a 0.124-kg baseball, and it approaches the bat at a speed of 54.2 m/s. The bat does W_nc = 76.5 J of work on the ball in hitting it. Ignoring the air resistance, determine the speed of the ball after the ball leaves the bat and is 21 m above the point of impact.

Homework Equations

W = E - E₀

The Attempt at a Solution

W = E -E_o
76.5=.5(.124)v²-.124(9.8)21
102.0192=.062v²
v = wrong answer!
Please help. I don't have a basics in physics, so please explain from an beginners standpoint.
Thankyou!

 

[rock.freak667]

The Attempt at a Solution

W = E -E_o
76.5=.5(.124)v²-.124(9.8)21
102.0192=.062v²
v = wrong answer!

where did you get 9.8 from? It told you 54.2 m/s was the initial velocity. Redo this part. For the second part you need to use projectile motion equations.

 

[agadag]

I used the eqn W=E-E₀, since they gave us a non conservative value.
this can b furthere broken down to... 1/2mv² -mgh. Thats where the 9.8 comes from. As far as projectile motion..how would i use it with no angles?

 

[rock.freak667]

I used the eqn W=E-E₀, since they gave us a non conservative value.
this can b furthere broken down to... 1/2mv² -mgh. Thats where the 9.8 comes from. As far as projectile motion..how would i use it with no angles?

actually as I think about it now, you don't need to use projectile motion.

Initially

all you have is that that change in kinetic energy = work done by that bat.

the initial ke = 1/2m(54)².

For the second part you need to use the part in red

 

[agadag]

Im confused. I got KE = 180.792. however, I am trying to find final velocity of the ball. i initially tried the eqn in red and it did not work for me. Can you please demonstrate?

 

[rock.freak667]

Im confused. I got KE = 180.792. however, I am trying to find final velocity of the ball. i initially tried the eqn in red and it did not work for me. Can you please demonstrate?

Conservation of energy right

Initially it has ke given by 1/2mu². This energy is converted into kinetic energy (it is moving with a different velocity v) and work done by the bat.

so applying the law of conservation of energy we will get 1/2mu²=1/2mv²+W_bat.

So can you find 'v' given W_bat=76.5J and u=54.2m/s?