3. A rocket is launched vertically from the ground with an initial velocity of 64 ft / sec . ( a ) Write a quadratic function h ( t ) that shows the height , in feet , of the rocket t seconds after it was launched . ( b ) Graph h ( t ) on the coordinate plane . ( c ) Use your graph from Part 3 ( b ) to determine the rocket's maximum height , the amount of time it took to reach its maximum height , and the amount of time it was in the air . Answer :

See below.

Step-by-step explanation:

The rocket's  flight is controlled by its initial velocity and the acceleration due to gravity.

The equation of motion is h(t) = ut + 1.2 g t^2 where  u = initial velocity, g = acceleration due to gravity ( = - 32 ft s^-2) and t = the time.

(a) h(t) = 64t  - 1/2*32 t^2

h(t) = 64t - 16t^2.

(b) The graph will be a parabola which opens downwards  with a maximum at the point (2, 64) and x-intercepts at (0, 0) and (4, 0).

The y-axis is the height of the rocket and the x-axis  gives the time.

Maximum height = 64 feet, Time to maximum height = 2 seconds, and time in the air = 4 seconds.