A model rocket is launched with an initial upward velocity of 215 ft/s. The rocket's height h (in feet) after t seconds is given by the following.

h=215t-16t^2

Find all values of t for which the rocket's height is 97 feet.

Given:

h=215t-16t^2

the rocket's height is 97 feet.

Substituting the value of h.

97 = 215 t-16 t^2

Rearranging,

-16 t^2 - 97 + 215 t = 0

or

16 t^2 - 215 t + 97 = 0

Solving the equation using quadratic formula:

We get two values of t.

t = 12.97

t = 0.46