Question

A ball is kicked from a height of 3 feet above the ground. The height of the ball, h (t), is given byh (t) =-512 + 14t + 3, where t is the time in seconds after the ball is kicked. How long will it takethe ball to hit the ground after it is kicked?

Answer 1

GIVEN

The function representing the path of the ball is given to be:

$h(t)=-5t^2+14t+3$

SOLUTION

The time taken to hit the ground can be calculated by equating the function to 0:

$h(t)=0$

Therefore:

$-5t^2+14t+3=0$

The quadratic equation can be solved as follows:

$\begin{gathered} Factor\text{ the equation:} \\ -\left(5t+1\right)\left(t-3\right)=0 \\ Apply\text{ the zero factor principle} \\ \therefore \\ 5t+1=0,t=-\frac{1}{5} \\ or \\ t-3=0,t=3 \end{gathered}$

Since the time can only be positive