2. A rock is thrown vertically upward with an initial velocity of 20 m/sfrom a bridge that is 25 meters above a river bed. Based on Newton'sLaws of motion, the height of the rock (above the river) t secondsafter being launched is given by:h(t) = -5t² + 20 t + 25 meters.(a) Determine the exact time, tr, at which the rock hits the river by solving the equationh (t) = 0 for t.(b) Sketch a graph of y = h (t) for 0≤t≤t seconds.(c) Using your graph from (b), deduce the maximum height attained by the rock abovethe 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 therock 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),whereAhh' (1) = lim= limAt-0 At. At-0(h(₁.(¹).h(1 + At) - h(1)AtEvaluate 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)

According to guidelines i solve first 3 subparts. So kindly request you to repost the remaining…

Answered: (a) Determine the exact time, tr, at…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(a) Determine the exact time, tr, 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≤t seconds. (c) Using your graph from (b), deduce the maximum height attained by the rock above the river.