Question

A thin stream of water flows smoothly from a faucet and falls straight down. at one point, the water is flowing at a speed of [u, = 1.63 m/s. at a lower poin, the diameter of the stream has decreased by a factor of 0.805. what is the verical lisance h between these two points?

Answer 1

The vertical distance between the two points is 0.1364 m.

Step-by-step explanation:

To find the vertical displacement between the two points, we can use the conservation of energy principle. The change in potential energy (mgh) is equal to the change in kinetic energy (1/2 * mu^2), where m is the mass of the water and u is the speed of the water.

Since the diameter of the stream decreases by a factor of 0.805, we can assume that the mass of the water remains constant. Therefore, the change in potential energy is equal to the change in kinetic energy:

mgh = 1/2 * mu^2

Solving for h, we get:

h = u^2 / (2g)

Substituting the given values of u = 1.63 m/s and taking the acceleration due to gravity as g = 9.8 m/s^2, we can calculate the vertical displacement h.

h = (1.63^2) / (2 * 9.8) = 0.1364 m

Therefore, the vertical distance between the two points is 0.1364 m.