How to find energy if mass and height is given?

[Echy14]

If you are going to throw a 1kg ball vertically upward and reach a maximum height of 18m. A)How much energy is needed?
B)What should be the initial speed of the ball?

My solution:
mgh=1/2mv^2
v=√2gh
v=√2(9.8)(18)
v=18.78m/s

In getting the energy
I derived the work energy theorem
2w=vo^2
2w=18.78^2
w=176.34 joules
I'm not sure if my answer is correct so I would be extremely grateful if someone could check it.

Thanks.

 

[Hootenanny]

If you are going to throw a 1kg ball vertically upward and reach a maximum height of 18m. A)How much energy is needed?
B)What should be the initial speed of the ball?

My solution:
mgh=1/2mv^2
v=√2gh
v=√2(9.8)(18)
v=18.78m/s

Correct.

In getting the energy
I derived the work energy theorem
2w=vo^2
2w=18.78^2
w=176.34 joules

By my reckoning, you are a decimal place off. It is likely a result of your rounding off the velocity.

Note that instead of using the velocity, you could have simply used the fact that work = change in energy = mgh. Do you see?

 

[Echy14]

Thanks for the quick reply.

Regarding on the fact that you had just said, that was actually my first solution but seeing that they both have the same result. I decided to use this one instead.