Question

A ball is throw into the air from an initial height of $10$ feet. Its height above the ground, in feet, $t$ seconds after it is thrown is given by the function $h\left(t\right)=16t^2+27t-10$. How long will it take (in seconds) for the ball to hit the ground after it is thrown?

• A. $-\frac{5}{16}$ seconds
• B. $2$ seconds
• C. $2\frac{1}{2}$ seconds
• D. $3$
• E. $\frac{5}{16}$ seconds

Answer 1

The correct option is B $2$ seconds

The ball would reach the ground when height $ht\left(t\right)=0$
$\Rightarrow 16t^2-27t-10=0$
$\Rightarrow 16t^2-32t+5t-10=0$
$\Rightarrow 16t(t-2)+5(t-2)=0$
$\Rightarrow (t-2)(16t+5)=0$
$\Rightarrow t=2$ or $t=-\frac{5}{16}$
Since number of seconds cannot be negative, time when the ball hits the ground is $2$ seconds.