Answer:
t=12.97 seconds
t=0.47 seconds
Step-by-step explanation:
Given :
A model rocket is launched with an initial upward velocity of 215 ft/s.
The rocket's height h (in feet) after t seconds : [tex]h=215t-16t^2[/tex]
To Find:
Find all values of t for which the rocket's height is 97 feet.
Solution :
[tex]h=215t-16t^2[/tex]
Since we are given that height = 97 feet
[tex]97=215t-16t^2[/tex]
[tex]16t^2-215t+97=0[/tex]
Using quadratic formula : [tex]t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
a = 16
b = -215
c = 97
[tex]t=\frac{215\pm\sqrt{(-215)^2-4\times16\times 97}}{2\times 16}[/tex]
[tex]t=\frac{215\pm\sqrt{40017}}{32}[/tex]
t = 12.970077983916697359451253891375
t = 0.46742201608330264054874610862542
Thus all values of t for which the rocket's height is 97 feet:
t=12.97 seconds
t=0.47 seconds
