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water flows through a garden hose which is attached to a nozzle. the water flows through hose with a speed of 1.89 m/s and through the nozzle with a speed of 35.3 m/s. calculate the maximum height (in m) to which water could be squirted if it emerges from the nozzle and emerges with the nozzle removed.

User Pokrate
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The maximum height to which water could be squirted is 63.44 m.

To calculate the height to which water could be squirted, we can use the principle of conservation of energy. When the water emerges from the nozzle, it will have both kinetic energy and potential energy. At the maximum height, all of the water's kinetic energy will have been converted into potential energy.

The equation for potential energy is given by PE = mgh, where m is the mass of the water, g is the acceleration due to gravity, and h is the height. To find the height, we need to know the mass of the water and the acceleration due to gravity. Since the problem doesn't provide the mass, we can assume a value of 1 kg for simplicity. The acceleration due to gravity is approximately 9.8 m/s^2.

Plugging these values into the equation, we get PE = (1 kg)(9.8 m/s^2)(h), which simplifies to PE = 9.8h. We know that the water flows through the nozzle with a speed of 35.3 m/s, which gives it a certain amount of kinetic energy. This kinetic energy can be expressed as KE = 0.5mv^2, where v is the velocity of the water. Plugging in the values, we get KE = 0.5(1 kg)(35.3 m/s)^2. This gives us the equation KE = 0.5(35.3)^2.

At the maximum height, all of the kinetic energy will have been converted into potential energy, so we can set KE equal to PE and solve for h. 0.5(35.3)^2 = 9.8h. Solving for h, we get h = 63.44 m.

Therefore, the maximum height to which water could be squirted is 63.44 m.

User Seabass
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