
import numpy as np

# Given parameters
m = 2.00  # mass in kg
v0 = 4.00  # initial velocity in m/s
U0 = 0  # initial potential energy in J
U1 = 7.0  # final potential energy in J

# Calculations
K0 = 0.5 * m * v0**2  # initial kinetic energy
Emec = K0 + U0  # initial mechanical energy
K1 = Emec - U1  # final kinetic energy

# Because K1 = 0.5 * m * v1^2, we find v1
v1 = np.sqrt(2 * K1 / m)  # final velocity

print(v1)
