How Do You Calculate the Initial Velocity of Water from a Drinking Fountain?

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SUMMARY

The initial velocity of water exiting a drinking fountain can be calculated using kinematic equations and trigonometric functions. The user measured a horizontal distance (dx) of 13.2 cm and a maximum height of 8.8 cm. By applying the equation V2^2 = V1^2 + 2ad, the vertical component of velocity (V1y) was determined to be 13.3 m/s. The angle of projection was calculated as 53 degrees, leading to a horizontal component (V1x) of 9.89 m/s, ultimately allowing for the calculation of the initial velocity (V1) using the Pythagorean theorem.

PREREQUISITES
  • Understanding of kinematic equations, specifically V2^2 = V1^2 + 2ad
  • Knowledge of trigonometric functions, particularly tangent and its application in angle calculations
  • Familiarity with unit conversions, especially between centimeters and meters
  • Proficiency in using the Pythagorean theorem for vector calculations
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  • Review the derivation and application of kinematic equations in projectile motion
  • Study the principles of projectile motion, focusing on the relationship between angle, height, and distance
  • Learn about unit conversion techniques, particularly in physics problems
  • Explore advanced projectile motion problems involving air resistance and varying angles
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Students studying physics, particularly those focusing on mechanics and projectile motion, as well as educators looking for practical examples of kinematic equations in real-world applications.

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Homework Statement



Calculate the initial velocity at which water exits the spout of a common drinking fountain

Homework Equations



V1x=V1cosΘ Θ=tan-1 (opp/adj)
V1y=V1sinΘ

V2^2=V1^2+2ad

The Attempt at a Solution



I measured the total distance traveled by the water in the x-direction (dx), and I got 13.2 cm. I also measured the maximum height and got 8.8cm. I used the kinematic formula (V2y^2=V1y^2+2aydy), so I had:

V2y^2=V1y^2+2aydy
0=V1y^2+2(-9.8)(8.8)
V1y= 13.3 m/s

I calculated the angle using the tan formula, so I got:
Θ=tan-1(opp/adj)
Θ=tan-1 (8.8/6.6)
Θ=53 degrees

Since I had the angle and V1y, I used these two to get V1x:

tanΘ=V1y/V1x
V1xtan53=13.3
V1x= 9.89m/s

Then I just used the pythagorean theorem to solve for V1. Would my method be correct?
 
Physics news on Phys.org
You are careless with your units and have omitted them from your calculations.
What are the units of g? What units were your measurements of the stream made in?
 

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