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 : \(h=215t-16t^2\)
To Find:
Find all values of t for which the rocket's height is 97 feet.
Solution :
\(h=215t-16t^2\)
Since we are given that height = 97 feet
\(97=215t-16t^2\)
\(16t^2-215t+97=0\)
Using quadratic formula : \(t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
a = 16
b = -215
c = 97
\(t=\frac{215\pm\sqrt{(-215)^2-4\times16\times 97}}{2\times 16}\)
\(t=\frac{215\pm\sqrt{40017}}{32}\)
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
