Tyreke is an engineer and needs to design a rocket for an experiment. He has calculated that the height of the rocket, in feet, with respect to time,
can be modeled by the equation h(t) = -16t^2 + vt + h0, where t is the time in seconds, v is the initial velocity of the rocket in feet per second, and h0 is the initial height of the rocket in feet.
To design the rocket, Tyreke needs to determine the initial velocity and initial height that will allow the rocket to reach a desired height within a specific time frame.
To find the initial velocity, Tyreke needs to know the desired height and the time it should take for the rocket to reach that height. The initial velocity can be found by rearranging the equation h(t) = -16t^2 + vt + h0 and solving for v.
v = (h(t) - h0) / t
Once Tyreke knows the initial velocity, he can determine the initial height by using the equation h(t) = -16t^2 + vt + h0 and solving for h0.
h0 = h(t) - vt
By plugging in the desired height and time, Tyreke can calculate the initial velocity and initial height needed for the rocket to reach the desired height within the specified time frame.