ANSWER
[tex]80 {ms}^{ - 1} [/tex]
EXPLANATION
The average velocity of the ball is the rateof displacement over the total time.
The height of the ball, in feet, after t seconds is given by the function:
[tex]f(t)=-16t^2+192t[/tex]
At time t=1, the height of the ball is
[tex]f(1)=-16(1)^2+192(1)[/tex]
[tex]f(1)=-16+192 = 176ft[/tex]
At time t=6, the height of the ball is
[tex]f(6)=-16(6)^2+192(6)[/tex]
[tex]f(6)=-16(36)+192(6)[/tex]
[tex]f(6)=-576+1152 = 576[/tex]
The average velocity
[tex] = \frac{f(6) - f(1)}{6 - 1} [/tex]
[tex]= \frac{576- 176}{6 - 1} [/tex]
[tex]= \frac{400}{5} [/tex]
[tex] = 80 {ms}^{ - 1} [/tex]
