Consider the following description of the vertical motion of an object subject t
ID: 2893184 • Letter: C
Question
Consider the following description of the vertical motion of an object subject to only acceleration due to gravity. Begin with the acceleration equation 2. a(r)-r(t)-g where g--98 p)-ve)-g where g--9)8 meters per second squared (m/'), Astone iS )-g where8 -9.8 meters per second squared (m/s').A stone is thrown vertically upward with an initial velocity of 30 meters per second (m/s) from the edge of a cliff 200 meters (m) above a river. Find the following: a. the velocity function, v(). Show full details. (6 points) b. the position function, st). Show full details. (6 points)Explanation / Answer
2)
a(t)=v'(t)=-9.8 , v(0)=30, s(0)=200
a)
v(t)=a(t) dt
v(t)=(-9.8) dt
v(t)=(-9.8t)+c
v(0)=30
=>(-9.8*0)+c=30
=>c=30
v(t)=(-9.8t)+30
velocity function is v(t)=(-9.8t)+30
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b)
s(t)=v(t) dt
s(t)=((-9.8t)+30) dt
s(t)=(-4.9t2)+(30t) +c
s(0)=200
=>(-4.9*02)+(30*0) +c=200
=>c=200
position fuction is s(t)=(-4.9t2)+(30t) +200
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c)
at highest point v(t)=0
=>(-9.8t)+30=0
=>t=30/9.8
=>t=3.06
object reaches highest point after 3.1 seconds
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d) maximum height = s(3.06)
maximum height = (-4.9*(3.06)2)+(30*(3.06)) +200
maximum height =245.955
maximum height is 246 meters