Question

1) A ball is thrown downward from a window in a tall building. Its position at time t in seconds iss(t) = -16t2 + 32t + 55, where s(t) is in feet. How long (to the nearest tenth) will it take the ball to hit the ground?A)-1.2 secB) 1.2 secC) 2.9 secD) 3 sec

Answer 1

The equation for the position is,

$s(t)=-16t^2+32t+55$

When the ball hit the ground then value of height is 0 feet. So value of s(t)=0,

The equation for the time is,

$-16t^2+32t+55=0$

Determine the roots of the equation by using the quadratic formula.

$\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ =\frac{-32\pm\sqrt[]{(32)^2-4(-16)(55)}}{2(-16)} \\ =\frac{-32\pm\sqrt[]{4544}}{-32} \\ =\frac{-32\pm67.41}{-32} \\ =\frac{-99.41}{-32},\text{ }\frac{35.41}{-32} \\ =3.10,-1.10 \end{gathered}$

The value of time can never be less than 0. so approximate value of time is 3 seconds. Correct option is D part.