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brewAP2010
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"Calculus of lawn sprinklers"
A lawn sprinkler is constructed in such a way that dθ/dt is constant, where θ ranges between 45⁰ and 135⁰. The distance the water travels horizontally is x= (v^2sin2θ)/32, 45⁰ < θ < 135⁰ where v is the speed of the water. Find dx/dt and explain why this lawn sprinkler does not water evenly. What part of the lawn receives the most water?
If I’m not mistaken the velocity of the water should be a constant so v^2/32 is a coefficient, and when you derive dx/dt=(v^2/32)cos2θ(2dθ/dt).
Homework Statement
A lawn sprinkler is constructed in such a way that dθ/dt is constant, where θ ranges between 45⁰ and 135⁰. The distance the water travels horizontally is x= (v^2sin2θ)/32, 45⁰ < θ < 135⁰ where v is the speed of the water. Find dx/dt and explain why this lawn sprinkler does not water evenly. What part of the lawn receives the most water?
Homework Equations
The Attempt at a Solution
If I’m not mistaken the velocity of the water should be a constant so v^2/32 is a coefficient, and when you derive dx/dt=(v^2/32)cos2θ(2dθ/dt).