Explanation Given: The maximum height is h = v 2 1960 cm . Formula used: Linear approximation of Δ f : If f is differentiable at x = a and Δ x is small then Δ f ≈ f ′ ( a ) Δ x Where Δ f = f ( a + Δ x ) − f ( a ) . Calculation: The maximum height is h = v 2 1960 cm . Part a: We have to apply the linear approximation with a = R and Δ x = h . Use the formula: Δ f ≈ f ′ ( a ) Δ x We can rewrite the formula as: Δ h ≈ h ′ ( v ) Δ v Differentiate the function with respect to v . h ′ ( v ) = v 980 Now, find the linear approximation when v = 700 cm / s and Δ v = 1 cm / s . Δ h ≈ h ′ ( v ) Δ v ≈ h ′ ( 700 ) ( 1 ) = 700 980 ( 1 ) = 0

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.1, Problem 43E

To determine

a. Estimate Δh if v=700 cm/s and Δv=1 cm/s.

b. Estimate Δh if v=1000 cm/s and Δv=1 cm/s.

c. Does a 1 cm/s increase in v lead to a greater change in h at low or high initial velocity. Also, explain.

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Chapter 4.1, Problem 42E

Chapter 4.1, Problem 44E

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a. Estimate Δ h if v = 700 cm / s and Δ v = 1 cm / s . b. Estimate Δ h if v = 1000 cm / s and Δ v = 1 cm / s . c. Does a 1 cm / s increase in v lead to a greater change in h at low or high initial velocity. Also, explain.

Solution Summary: The author explains the linear approximation of Delta f.

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a. Estimate Δh if v=700 cm/s and Δv=1 cm/s.

b. Estimate Δh if v=1000 cm/s and Δv=1 cm/s.

c. Does a 1 cm/s increase in v lead to a greater change in h at low or high initial velocity. Also, explain.

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Chapter 4 Solutions

a. Estimate Δ h if v = 700 cm / s and Δ v = 1 cm / s . b. Estimate Δ h if v = 1000 cm / s and Δ v = 1 cm / s . c. Does a 1 cm / s increase in v lead to a greater change in h at low or high initial velocity. Also, explain.

Solution Summary: The author explains the linear approximation of Delta f.

Concept explainers

Videos

a. Estimate Δh if v=700 cm/s and Δv=1 cm/s. b. Estimate Δh if v=1000 cm/s and Δv=1 cm/s. c. Does a 1 cm/s increase in v lead to a greater change in h at low or high initial velocity. Also, explain.

Want to see the full answer?

Chapter 4 Solutions

a. Estimate Δh if v=700 cm/s and Δv=1 cm/s.

b. Estimate Δh if v=1000 cm/s and Δv=1 cm/s.

c. Does a 1 cm/s increase in v lead to a greater change in h at low or high initial velocity. Also, explain.