Question

At a model rocket competition, Mrs. Jennings launches a rocket is launched upward

from the ground with an initial velocity of 138 feet per second.
The formula for vertical motion is
h(t) = 0.5at? + vt +s, where the gravitational constant, a, is -32 feet per second squared, v
is the initial velocity, and s is the initial height. Time t is measured in seconds, velocity
v is measured in feet per second, and heights h and s are measured in feet.
Write the function that describes the height, h in feet, of the rocket l seconds into
launch

Answer 1

The function that describes the height, h in feet, of the rocket, t seconds into launch is h = -16·t² + 138·t

Explanation:

The given parameters are;

The initial velocity of the rocket, v = 138 feet per second

The vertical motion formula = h(t) = 0.5·a·t² + v·t + s

The gravitational constant, a = -32 ft./s²

s = The initial height of the rocket

Therefore, he have;

The height of the rocket, t seconds seconds into launch is given as follows;

Height = h = h(t) - s = 0.5·a·t² + v·t

Substituting the known values gives;

h(t) - s = 0.5 × (-32) × t² + 138 × t = -16·t² + 138·t

h = -16·t² + 138·t

The function that describes the height, h in feet, of the rocket, t seconds into launch is h = -16·t² + 138·t.