please help me!!!

Question

The function g(t) = - 16t ^ 2 + vt + h represents the height of an object, , in feet above the ground in relation to the time, t, in seconds , since the object was thrown into the air with an initial velocity of v feet per second at an initial height of h feet . A model rocket is launched off the ground at an initial velocity of 80 feet per second.

what domain makes sense for the function

Answer 1

-16t^2 + 80t + h

take the derivative and set =0 and solve for t

-32t +80 = 0

max height is when t =80/32 = 10/4 = 2.5 seconds

if h=0, it hits ground in twice the time or 5 seconds

but if h doesn't = zero, such as h>0 then

-16t^2 + 80t + h = 0

2t^ -10t -h/16 = 0

t^2 -5t = h/16

(t-5/2)^2 = h/16+25/4

t-5/2 = (1/4)sqr(h+100)

t = 5/2 + (1/4)sqr(h+100)

so the domain is 0 < 5/2+(1/4)sqr(h+100) which has no limit if h has no limit

Answer 2

The domain would be values of t that make sense for the equation. The variable t would be from launch at for t=0 until it hit the ground again. So the domain of t would be found by solving for t in:

g(t) = -16t² + 80t + h = 0

We probably can assume the initial height, h is ground level = 0.

t(-16t +80) = 0, t = 0, 80/16=5

The domain of t would be from t=0 to 5 seconds.