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Answer :
The rocket will take 9.25 seconds to return to ground
Solution:
Given that toy rocket is launched vertically upward from ground level with an initial velocity of 148 ft per second
Height "h" after "t" seconds is given by equation:
[tex]h(t) = -16t^2 + 148t[/tex]
To find: time taken by rocket to return to ground
The time taken by rocket to return to ground is found by substituting h(t) = 0 in above equation
[tex]0 = -16t^2 + 148t[/tex]
First take "t" as common term
[tex]t(-16t + 148) = 0[/tex]
Zero product property. The zero product property states that if a⋅b = 0 then either a or b equal zero. This basic property helps us solve equations like (x+2)(x-5) = 0
So for above equation we get,
[tex]t = 0 \text{ or } -16t + 148 = 0[/tex]
-16t + 148 = 0
-16t = -148
t = 9.25
When t = 0 , the rocket would not left the ground. So ignore t = 0
So t = 9.25
So the rocket will take 9.25 seconds to return to ground
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