Vertical Motion In r() =-16a + \'e, + Kg for free-falling object silver dollar i

Question

Vertical Motion In r() =-16a + 'e, + Kg for free-falling object silver dollar is dropped from the top of a building 1362 feet tall. e95,A (a) Determine the position and velocity functions for coin. (b) Determine the average velocity on the interval [ (e) Find the instantaneous velocities when 1-Indr2 (d) Find the time required for the coin to reach (e) Find the velocity of the coin at impact ground leve r 96. A ball is thrown straight down from the top of a220to building with an initial velocity of-22 feet per what is its velocity after 3 seconds? What is its velocity falling 108 feet? Vertical Motion In Exercises 97 and 98, use the function su) =-40f + 97)A projectile is shot upward from the surface of Earth + so for free-falling objects. e initial velocity of 120 meters per second. What is its veloct after 5 seconds? After 10 seconds? 98. A rock is dropped from the edge of a cliff that is 214 mete above water. (a) Determine the position and velocity functions for the rock b) Determine the average velocity on the interval [2.5) (c) Find the instantaneous velocities when-2 and r-5 (d) Find the time required for the rock to reach the surface of the water (c) Find the velocity of the rock at impact 99)hink About lt The graph of the position functin see figure) represents the distance in miles that a perscn drives during a 10-minute trip to work. Make a sketch of the corresponding velocity function. 10 60 20 10 (6, 2) (0,0) 2 4 6 810 246810 Time (in minutes) Time (in minuties) Figure for 9 Figure for 100 100. Think About It The graph of the velocity function (sct figure) represents the velocity in miles per hour during a 10-minute trip to work. Make a sketch of the position function 101. Volume The volume of a cube with sides of length s is given by V=53. Find the rate of change of the volume wit respect to s when s = 6 centimeters. The area of a square with sides of length s is by A s. Find the rate of change of the arca with resp swhen s- 6 meters

Explanation / Answer

multiple questions posted.please post each question seperately
95)

vo=0, so=1362

(a)

position,s(t) =-16t2 +0t+1362

position,s(t) =-16t2 +1362

velocity ,v(t)=s'(t)

velocity ,v(t)=-16*2t +0

velocity ,v(t)=-32t

(b)

average velocity on interval [1,2] is =[s(2)-s(1)]/(2-1)

average velocity on interval [1,2] is =[(-16*22 +1362)-(-16*12 +1362)]/(2-1)

average velocity on interval [1,2] is = - 48 feet/second

(c)

instantaneous velocity when t=1 is =v(1)

instantaneous velocity when t=1 is =-32*1

instantaneous velocity when t=1 is =-32 feet/second

instantaneous velocity when t=2 is =v(2)

instantaneous velocity when t=2 is =-32*2

instantaneous velocity when t=2 is =-64 feet/second

(d)

on the ground ,s(t)=0

=>-16t2 +1362=0

=>t2 =1362/16

=>t =(681/8)

=>t =9.226 seconds approximately

(e)

velocity of impact =v((681/8))

velocity of impact=-32*(681/8)

velocity of impact=-295.24 feet/second approximately

=================================================================

97)

so=0,v0=120

s(t)=-4.9t2+120t +0

s(t)=-4.9t2+120t

velocity ,v(t)=s'(t)

velocity ,v(t)=-4.9*2t +120*1

velocity ,v(t)=-9.8t +120

velocity after 5seconds =v(5)

velocity after 5seconds =-9.8*5 +120

velocity after 5seconds =71 meters/second

velocity after 10seconds =v(10)

velocity after 10seconds =-9.8*10 +120

velocity after 10seconds =22 meters/second

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