Water comes down the spillway of a dam from an initial vertical height of 170 m.What is the highest possible speed of the water at the end of the spillway?
A)5.89 m/s
B)18.4 m/s
C)57.7 m/s
D)1 670 m/s
E)3 330 m/s

Question

Quizplus · Accepted Answer

The height h of the water can be used to calculate the potential energy, which is converted to kinetic energy at the bottom of the spillway. The kinetic energy equation is:

KE = 1/2 * m * v^2

where m is the mass of the water (which we can assume to be 1 kg per unit volume) and v is the velocity.

Using conservation of energy, we can set the potential energy at the top of the spillway (mgh) equal to the kinetic energy at the bottom (1/2 * mv^2):

mgh = 1/2 * mv^2

Canceling out the mass, we get:

gh = 1/2 * v^2

Solving for v, we get:

v = sqrt(2gh)

Plugging in the values given, we get:

v = sqrt(2*9.8*170) = 57.7 m/s

Therefore, the highest possible speed of the water at the end of the spillway is 57.7 m/s, which is choice C.

Water Comes Down the Spillway of a Dam from an Initial