Calculating Maximum Height and Final Velocity: 2 Energy Problems on a Slope

[rain_ex]

Homework Statement

A 50g ice cube has no friction. It compresses a string with the constant 25 N*m a total of 10 cm. Find the max height reached by the ice cube before it starts sliding back down the slope, after it is released from the spring.

Known:
m = 50g (.05kg)
k = 25 Nm
x = 10cm (.1m)

Homework Equations

E₀ = E <- general
Us₀ = Ug <- expanded
1/2kx² = mgh <- final equation

The Attempt at a Solution

I ended up with 0.255m. Is this correct? I solved for the variable "h".

Homework Statement

A cannon angled 30 degrees above the horizontal launches a cannanball at 80 m/s. if the cannon is 10 m above the ground with what speed does the cannon ball strike the ground?

Homework Equations

E₀ = E <- general
Ug₀ + K₀ = K <- expanded
mgh+1/2mv₀² = 1/2mv² <-final equation

The Attempt at a Solution

I ended up with 81.216 m/s. I solved for the variable "v".

Please check my solutions for me! Thank you!

 

[ehild]

Your solution is correct, but the unit of the spring constant k is N/m instead of Nm.

ehild

 

[rain_ex]

Thank you.
I'm assuming that the 2nd question's solution was correct too?

 

[ehild]

Yes, both solutions are correct.

ehild