Water flows out horizontalmy at the end of a pipe at a height of 52 cm from the floor.If the horizontal distance before it hits the floor is 100 cm,calculate the velocity of the water at the instant it leaves the pipes?

How long does it take to hit the floor. That is S = distance = 1/2*g*t^2 and S is 52 cm (0.52 m). Solve for t.

Then distance = rate*time
distance s 100 cm = 1 m, time from above, solve for rate.

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Water flows out horizontalmy at the end of a pipe at a height of 52 cm from the floor.If the horizontal distance before it hits the floor is 100 cm,calculate the velocity of the water at the instant it leaves the pipes?

To calculate the velocity of the water at the instant it leaves the pipe, we can use the principles of projectile motion.

Let's assume that the initial vertical velocity of the water is zero, as it is flowing purely horizontally.

First, we need to calculate the time it takes for the water to reach the floor. We can use the equation for vertical motion:

h = (1/2) * g * t^2

Where:
h = vertical height (52 cm in this case)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time

Converting the height to meters (1 m = 100 cm), we have:

h = 0.52 m

Rearranging the equation, we can solve for t:

t^2 = (2 * h) / g
t^2 = (2 * 0.52 m) / 9.8 m/s^2
t^2 = (1.04 m) / 9.8 m/s^2
t^2 ≈ 0.1061 s^2
t ≈ 0.326 s

Now that we have the time it takes for the water to reach the floor, we can calculate the horizontal distance it travels using the formula:

d = v * t

Where:
d = horizontal distance (100 cm = 1m)
v = horizontal velocity (what we want to find)
t = time (0.326 s)

Rearranging the equation, we can solve for v:

v = d / t
v = 1 m / 0.326 s
v ≈ 3.07 m/s

Therefore, the velocity of the water at the instant it leaves the pipe is approximately 3.07 m/s in the horizontal direction.

To calculate the velocity of the water at the instant it leaves the pipe, we can use the principle of conservation of energy.

The energy at two points in the system will remain constant: the initial point where the water leaves the pipe and the final point where it hits the floor. At the initial point, the energy is in the form of potential energy, while at the final point, it is kinetic energy.

The potential energy (PE) of an object is given by its height (h) and the force of gravity (g), which is approximately 9.8 m/s². The kinetic energy (KE) of an object is given by its mass (m) and velocity (v) using the formula KE = 0.5 * m * v².

Here's how we can calculate the velocity:

Step 1: Convert the height from cm to meters.
52 cm = 0.52 m

Step 2: Calculate the potential energy at the initial point using the formula PE = m * g * h.
PE = 0.52 * 9.8 * 0.52

Step 3: Calculate the kinetic energy at the final point, where the potential energy is converted to kinetic energy. Since both the initial and final points have the same mass, we can equate the potential and kinetic energies.
PE = KE
0.52 * 9.8 * 0.52 = 0.5 * m * v²

Step 4: Rearrange the equation to solve for velocity (v).
v² = (2 * PE) / m

Step 5: Substitute the values into the equation and solve for v.
v² = (2 * 0.52 * 9.8 * 0.52) / m

Step 6: The horizontal distance the water travels before hitting the floor is not required to calculate the velocity at the instant it leaves the pipe.

Note: To obtain the mass (m) of the water, additional information is needed, such as the density or volume of the water. Without this information, it is not possible to calculate the velocity.