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# RE Velocity of a rocket The height in feet of a rocket ## Problem 61RE Chapter 3

Calculus: Early Transcendentals | 1st Edition

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Problem 61RE

RE Velocity of a rocket? The height in feet of a rocket above the ground is given by s(t)= 202t2 for t? 0. t +1 a.? Graph the height function and describe the motion of the rocket. b.? Find the velocity of t? h?e roc ? k? t? (?t) =? ?(?t). c.? Graph the velocity function and determine the approximate time at which the velocity is a maximum.

Step-by-Step Solution:

Solution Step 1: The height in feet of a rocket above the ground is given by 200t2 s(t)= t +1for t 0 (a)The rocket climbs quickly at first so that it has attained a height of 160 by the time t=2, then climbs more slowly climbing less than 40 units between t=2 and t=4 Step 2 The graph of the height function is given below Step 3: The velocity of the rocket v(t) = s (t) d = dxt) = d [200t2 ] dt t +1 2 v(t) =200 dt [ 2t ] ….(1) t +1 We know that d d d [u(x) ]= v(x)dxu(x))u(2)dxv(x)) dx v(x) (v(x)) Step 4 By using this formula we can find the derivative (1) 2 v(t) =200 d [ 2t ] dt t +1 2 d 2 2 d 2 (t +1)dtt )(t dt(t +1) =200[ (t +1) ] 2 2 =200[ (t +1)(2t)(t )(2t] (t +1)2 =200[ 2t ] (t +1)2

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