Answer:
Option D. [tex]H(t) = 6.5+21t-16t^2[/tex]
Step-by-step explanation:
we know that
If air resistance is ignored, the height h (in feet) of the ball t seconds after it is served is given by
[tex]H(t) = - \frac{1}{2}g t^2 + V_0t + H_0[/tex]
where
g is the acceleration due to gravity which on earth is approximately equal to 32 feet / sec^2
V_0 is the initial velocity (when t = 0 )
H_0 is the initial height (when t = 0)
In this problem we have
[tex]V_0=21\ ft/sec\\H_0=6.5\ ft[/tex]
substitute the given values
[tex]H(t) = - \frac{1}{2}(32) t^2 + (21)t + 6.5[/tex]
[tex]H(t) = -16t^2 + 21t + 6.5[/tex]
Rewrite
[tex]H(t) = 6.5+21t-16t^2[/tex]
