Question

Hey guys, I have been having some trouble with this question related to quadratic formulas. Its a 3 part question, but I only want the first part done, so I can do the rest. Here is the question:
3. A rocket is launched vertically from the ground with an initial velocity of 64 .
(a) Write a quadratic function h(t) that shows the height, in feet, of the rocket t seconds after it was launched.

Thank you so much in advance. I really appreciate it.

Answer 1

To find the height that the rocket has reached, we can use the following equation to calculate distance.
s = ut + 1/2 at²
s - distance - h
u - initial velocity  - 64 ft/s x 0.3048 m/ft = 19.5 m/s
a - acceleration, since the rocket is travelling upwards against gravitational acceleration, its said to be deceleration. therefore value is -9.8 ms⁻²
t - time taken  - t seconds
substituting values in the equation
h = 19.5 ms⁻¹ x t s - 1/2 x 9.8 ms⁻² x (t s)²
h = 19.5t - 4.9t²