Answer: 12.4 feet
Step-by-step explanation:
If there is a smooth transition and there is no change in slopes, energy considerations can be used
The cube has a kinetic energy of
ke = mv^2/2 = 10 lbm * 20^2ft^2/s^2 / 2 = 2000 lbm-ft^2 / s^2
At the highest point when there is a gain in potential energy
pe = mgh = 10 lbm * 32.2 ft/s^2 * h ft = 322 lbm ft^2/s^2
If there is no loss in energies,
pe = ke
322h lbm ft^2/s^2 = 2000 lbm ft^2/s^2
h = 2000 /322 = 6.211 (ft)
= h / sin(30) = 12.4 ft