Question

The function which represents the height, $h\left(t\right)$, of a ball t seconds after it is kicked into the air is
$h\left(t\right)=-16t^2+64t$.
What does $t$ represent if $h\left(t\right)$ is zero ?

• A. Time that ball reaches $\frac{3^{th}}{4}$ its maximum height
• B. TIme that ball reaches one- half its maximum height
• C. The time at which the ball is on the ground
• D. Time that ball reaches its maximum height

Answer 1

Answer: (C)

The time at which the ball is on the ground

Answer is C.
The formula for the height H of a ball thrown upward is given by
$h\left(t\right)=-\frac{1}{2}g{t}^2+V_{0}t+H_0$
where, $t$ is the time taken.
In this case, the equation is given as $h\left(t\right)=$$-16t^2+64t$.
If $h\left(t\right)$ is zero, then the ball is at the ground $h=0$, hence the solution of the equation $h=0$ gives the time t at which the object hits the ground.
Hence, t represents the time at which the bail is on the ground if $h\left(t\right)$ is zero of this function.