A model rocket is launched with an initial velocity of 11 [c] feet per second fr
ID: 2920006 • Letter: A
Question
A model rocket is launched with an initial velocity of 11[c] feet per second from the height of [a] feet. The function s ( t ) = ? 16 t 2 + 11 [ c ] t + [ a ] models the path of the rocket where t represents the time, in seconds, after which the rocket is launched and s represents the height of the rocket at time t. My PIN is {a}=2, {b}=4, {c}=7, {d}=5, {e}=9.
Fill in the table of values for the function, and give a short interpretation for each point.
How long will it take for the rocket to return to the ground?
How long will it take the rocket to reach its maximum height? What is the maximum height reached by the rocket?
Round all answers to one decimal place.
Note: if [a]=2 and [c]=7, then s ( t ) = ? 16 t 2 + 117 t + 2
Work this custom problem about the quadratic function using the techniques you learned in this module.
Interpretation 0 2 4 10 150 150 200 200Explanation / Answer
s(t) = -16t2 + 117t + 2
on the ground s(t)=0
=> -16t2 + 117t + 2=0
=> 16t2 - 117t = 2
=> t2 - 2*(117/32)t = (2/16)
=> t2 - 2*(117/32)t +(117/32)2 = (2/16)+(117/32)2
=> (t - (117/32))2 = (13817/322)
=> (t - (117/32)) = ((13817)/32)
=> t = ((117+13817)/32)
=> t =7.329554243 seconds
it takes 7.3 seconds for the rocket to return to the ground
s(t) = -16t2 + 117t + 2
=> s'(t) = -32t + 117
at maximum height s(t)=0
=>-32t +117
=>t= 117/32
=>t=3.65625
it takes 3.7 seconds for the rocket to reach its maximum height
maxiumum height =s(3.65625)
maxiumum height = -16(3.65625)2 + 117(3.65625) + 2
maxiumum height = 215.891 feet
maximum height reached by the
rocket is 215.9 feet
please rate if helpful. please comment if you have any doubt
t s(t) interpretation 0 2 initial height is 2 feet 2 172 after 2seconds height is 172 feet 4 214 after 4seconds height is 214 feet 10 - 428 practically after 7.3 seconds rocket is already on ground 1.6 150 after 1.6seconds height is 150 feet 5.7 150 after 5.7seconds height is 150 feet 2.7 200 after 2.7seconds height is 200 feet 4.7 200 after 4.7seconds height is 200 feetRelated Questions
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