Question

A rock is thrown upward with an initial velocity of 16 ft/s from an initial height of 5 ft. write a quadratic function equation that describes the height h at time t.

Answer 1

The quadratic function equation that describes the height of the rock is h = -16t^2 + 16t + 5.

Step-by-step explanation:

To write a quadratic function equation that describes the height h at time t, we can use the kinematic equation for vertical motion: h = -16t^2 + 16t + 5. This equation represents the height of the rock as a function of time, taking into account the initial height, initial velocity, and acceleration due to gravity. The coefficient -16 in front of t^2 accounts for the downward acceleration of the rock.

Answer 2

During upward projection the final velocity is zero, and the gravitational acceleration is -10 m/s² (against the gravity).
Therefore; using the equation;
S = 1/2gt² + ut
Where s is the height h, g is gravitational acceleration, and t is the time and u is the initial velocity u, is 16 ft/s.
Thus; h= 1/2(-10)t² + 16t
We get; h = -5t² + 16t
Therefore; the quadratic equation is 5t² - 16t + h =0