A projectile with mass m is launched into the air on a parabolic trajectory. For t >0, its horizontal and vertical coordinates are r(t) = uot and y(t) = -}gt² + vot, respectively, where u, is the initial horizontal velocity, vo is the initial vertical velocity, and g is acceleration due to gravity. Recalling that u(t) = x' (t) and v(t) = y'(t) are the components of the velocity, the energy of the projectile (kinetic plus potential) is 2. E(t) = ;m(u² + v²) + mgy. Use the chain rule to compute E' (t) for t > 0, and simplify your result as much as possible. Interpret the result.

A projectile with mass m is launched into the air on a parabolic trajectory. For t >0, its horizontal and vertical coordinates are r(t) = uot and y(t) = -}gt² + vot, respectively, where u, is the initial horizontal velocity, vo is the initial vertical velocity, and g is acceleration due to gravity. Recalling that u(t) = x' (t) and v(t) = y'(t) are the components of the velocity, the energy of the projectile (kinetic plus potential) is 2. E(t) = ;m(u² + v²) + mgy. Use the chain rule to compute E' (t) for t > 0, and simplify your result as much as possible. Interpret the result.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

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