Question

a rock is dropped from a hot air balloon that is floating 1024 feet above the ground. the solution to the following equation will determine the number of seconds, t, the rock will fall until it hits the ground, assuming no wind resistance.
$-16t^2 + 1024 = 0$
how many seconds does it take for the rock to hit the ground?
check answer

Explanation:

Step1: Isolate the \( t^2 \) term

Start with the equation \(-16t^2 + 1024 = 0\). Subtract 1024 from both sides:
\(-16t^2 = -1024\)

Step2: Solve for \( t^2 \)

Divide both sides by -16:
\(t^2 = \frac{-1024}{-16} = 64\)

Step3: Solve for \( t \)

Take the square root of both sides. Since time cannot be negative in this context, we consider the positive square root:
\(t = \sqrt{64} = 8\)

Answer:

8