A plastic cup,15.0 cm in height,is filled to the rim with water and is resting on a table.A small hole is punctured in the cup at a height 9.00 cm above the bottom of the cup and is allowing water to spew out.What is the speed of the water when it strikes the table?

Question

Quizplus · Accepted Answer

We can use the principle of conservation of energy:
Initial energy = Final energy 
Initially, the only energy is the potential energy of the water:
Ei = mgh = (density of water)(volume of water)(g)(h)

Finally, the water has both potential and kinetic energy. At the moment it hits the table, all the potential energy is converted to kinetic energy:
Ef = (1/2)mv^2

We can equate these two energies and solve for v:
mgh = (1/2)mv^2 
Simplifying, we have:
v = sqrt(2gh)

We're given h = 15 cm - 9 cm = 6 cm = 0.06 m
We know g = 9.8 m/s^2
Plugging in these values, we get:
v = sqrt(2*9.8*0.06) = 1.72 m/s

Therefore, the answer is B.

A Plastic Cup,15