The graph below shows the height of a projectile t seconds after it is launched. If acceleration due to gravity is -16 ft/s2
which equation models the height of the projectile correctly?
h(t) = at2 + vt + h0

Correct option: fourth one -> h(t) = -16t2 + 32v + 5

Step-by-step explanation:

To find the equation h(t) we need to find the values of a, v and h0.

The value of a is already given (a = -16).

Now, we just need to use two of the three points given to find the other parameters:

point (1,21): t = 1 and f(t) = 21:

21 = -16 + v + h0

point (0,5): t = 0 and f(t) = 5

5 = 0 + 0 + h0

h0 = 5

Using this value of h0 in the first equation, we have:

21 = -16 + v + 5

v = 21 + 16 - 5 = 32

So the equation is:

h(t) = -16t2 + 32v + 5

Correct option: fourth one.