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An object is dropped from the top of a building that is 64 feet tall. 

Use s(t) = -16t^2 + v0t+s0 to find the following:

a. the position function

b. velocity function

c. time required for object to hit ground

d. velocity of object at impact

 

Thank you!

 Nov 20, 2018
 #1
avatar+20217 
0

a    you are given the position function

b     velocity function is the derivative of position fxn

c         time will be when s(t) = 0

d       When you have THAT time , substitute that value of 't' in to the velocity function from 'b'

 Nov 20, 2018
 #2
avatar+107348 
+1

s ' (t)   =  -32t + Vo

 

c

Vo  = 0     [ the object is dropped...so the initial velocity = 0 ]

So  =   initial height  = 64 ft

 

So we have

 

0   = -16t^2 + 64       add 16t^2 to both sides

 

16t^2   = 64       divide both sides by 16

 

t^2   = 4       take the positive root

 

t  = 2   (seconds to hit the ground)

 

 

 

d

 

Velocity at impact

 

-32(2)   =   -64 ft/ s

 

 

cool cool cool

 Nov 20, 2018

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