Answer:
![h=64t-4.9t^{2}](https://tex.z-dn.net/?f=h%3D64t-4.9t%5E%7B2%7D)
Please refer to the attached graph.
Step-by-step explanation:
Given that
Initial velocity of rocket = 64 and is launched vertically.
To find:
Quadratic equation in time to represent the height of rocket in feet.
Solution:
Unit of initial velocity is not given in the question statement, let the velocity be in feet/second only.
Initial velocity, u = 64 feet/s
The acceleration will be = -g because it is going opposite to gravitational force so it will be negative acceleration motion (speed will be decreasing) so -g will be the acceleration.
Formula for distance traveled is given as:
![s=ut+\dfrac{1}{2}at^2](https://tex.z-dn.net/?f=s%3Dut%2B%5Cdfrac%7B1%7D%7B2%7Dat%5E2)
Here Let us represent s by 'h'
a = -g = 9.8 m/![s^2](https://tex.z-dn.net/?f=s%5E2)
Let us put the known values in the formula:
![h=64t+\dfrac{1}{2}(-9.8)t^2\\\Rightarrow h =64t-4.9t^2](https://tex.z-dn.net/?f=h%3D64t%2B%5Cdfrac%7B1%7D%7B2%7D%28-9.8%29t%5E2%5C%5C%5CRightarrow%20h%20%3D64t-4.9t%5E2)
It is a quadratic equation, the equation represents the graph of a parabola.
Please refer to the attached graph.
Value of height is 0 at 0 second and ~13 seconds