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(d) Determine the average velocity of the rock, Ah, from time t = 1 to t = 2 seconds. Does this value overestimate or underestimate the instantaneous velocity of the rock at time t = 1 second? Explain your reasoning. (e) The instantaneous velocity of the rock at time t = 1 second is given by h'(1), where Ah h' (1) = lim = lim At-0 At. At-0 (h(₁. (¹). h(1 + At) - h(1) At Evaluate this limit quotient to find the speed of the rock at time t = 1 second. Express your answer in units of both m/s and ft/s. (1 meter≈ 3.28 feet)

(d) Determine the average velocity of the rock, Ah, from time t = 1 to t = 2 seconds. Does this value overestimate or underestimate the instantaneous velocity of the rock at time t = 1 second? Explain your reasoning. (e) The instantaneous velocity of the rock at time t = 1 second is given by h'(1), where Ah h' (1) = lim = lim At-0 At. At-0 (h(₁. (¹). h(1 + At) - h(1) At Evaluate this limit quotient to find the speed of the rock at time t = 1 second. Express your answer in units of both m/s and ft/s. (1 meter≈ 3.28 feet)

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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 (d) Determine the average velocity of the rock, Ah, from time t = 1 to t = 2 seconds. Does this value overestimate or underestimate the instantaneous velocity of the rock at time t = 1 second? Explain your reasoning. (e) The instantaneous velocity of the rock at time t = 1 second is given by h'(1), where Ah h' (1) = lim = lim At-0 At. At-0 (h(₁. (¹). h(1 + At) - h(1) At Evaluate this limit quotient to find the speed of the rock at time t = 1 second. Express your answer in units of both m/s and ft/s. (1 meter≈ 3.28 feet)

2. A rock is thrown vertically upward with an initial velocity of 20 m/s from a bridge that is 25 meters above a river bed. Based on Newton's Laws of motion, the height of the rock (above the river) t seconds after being launched is given by: h(t) = -5 t² + 20 t + 25 meters. (a) Determine the exact time, t, at which the rock hits the river by solving the equation h (t) = 0 for t. (b) Sketch a graph of y = h (t) for 0≤t≤tp seconds. (c) Using your graph from (b), deduce the maximum height attained by the rock above the river. (d) Determine the average velocity of the rock, Ah, from time t = 1 to t = 2 seconds. Does this value overestimate or underestimate the instantaneous velocity of the rock at time t = 1 second? Explain your reasoning. (e) The instantaneous velocity of the rock at time t = 1 second is given by h'(1), where h'(1) = lim At-0 At = lim At→0 h(1 + At) - h(1) At Evaluate this limit quotient to find the speed of the rock at time t = 1 second. Express your answer in units of both m/s and ft/s. (1 meter ≈ 3.28 feet)
Transcribed Image Text:2. A rock is thrown vertically upward with an initial velocity of 20 m/s from a bridge that is 25 meters above a river bed. Based on Newton's Laws of motion, the height of the rock (above the river) t seconds after being launched is given by: h(t) = -5 t² + 20 t + 25 meters. (a) Determine the exact time, t, at which the rock hits the river by solving the equation h (t) = 0 for t. (b) Sketch a graph of y = h (t) for 0≤t≤tp seconds. (c) Using your graph from (b), deduce the maximum height attained by the rock above the river. (d) Determine the average velocity of the rock, Ah, from time t = 1 to t = 2 seconds. Does this value overestimate or underestimate the instantaneous velocity of the rock at time t = 1 second? Explain your reasoning. (e) The instantaneous velocity of the rock at time t = 1 second is given by h'(1), where h'(1) = lim At-0 At = lim At→0 h(1 + At) - h(1) At Evaluate this limit quotient to find the speed of the rock at time t = 1 second. Express your answer in units of both m/s and ft/s. (1 meter ≈ 3.28 feet)
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