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