Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at which it is caught by Ryan. If we ignore air resistance, the horizontal range r of the baseball is a function of the initial speed v of the ball when it leaves Nolan's hand and the angle θ above the horizontal at which it is thrown. Use the accompanying table and the equations below to estimate the partial derivatives. fx(x0,y0)= limΔ⁢x→0f(x0+Δ⁢x,y0)-f(x0,y0)Δ⁢x; fy(x0,y0) =limΔ⁢y→0f(x0,y0+Δ⁢y)-f(x0,y0)Δ⁢y Take a left-hand estimate and a right-hand estimate in each case and give the average of the two as your final answer. (a) Estimate the partial derivative of r with respect to v when v=80ft/s and θ=45∘.

Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at which it is caught by Ryan. If we ignore air resistance, the horizontal range r of the baseball is a function of the initial speed v of the ball when it leaves Nolan's hand and the angle θ above the horizontal at which it is thrown. Use the accompanying table and the equations below to estimate the partial derivatives. fx(x0,y0)= limΔ⁢x→0f(x0+Δ⁢x,y0)-f(x0,y0)Δ⁢x; fy(x0,y0) =limΔ⁢y→0f(x0,y0+Δ⁢y)-f(x0,y0)Δ⁢y Take a left-hand estimate and a right-hand estimate in each case and give the average of the two as your final answer. (a) Estimate the partial derivative of r with respect to v when v=80ft/s and θ=45∘.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter3: Vectors

Section: Chapter Questions

Problem 59PQ

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