Answer:
a.) t = 16 seconds
b.) h(2) = 256 feet.
Step-by-step explanation:
a.)Bottle rocket height in feet is given by h(t) = 160t - 16[tex]t^2[/tex].
When the rocket returns to the ground its height will be zero.
Therefore we can write the equation above as
160t - 16[tex]t^2[/tex] = 0
⇒16t ( 16 - t) = 0
On solving the equation above we get two values for t which are
t = 0 seconds and t = 16 seconds.
We ignore t = 0 seconds because this is the starting time.
Therefore we can say that the rocket returns to the ground at time t = 16 seconds.
b.) The height in feet after 2 seconds will be given by
h(2 seconds) = (160 ×2) - (16 × [tex](2)^2[/tex] ) = 320 - 64 = 256 feet.
