an acorn falls from the branch of a tree to the ground 25 feet below. the distance, s, that the acorn is…

an acorn falls from the branch of a tree to the ground 25 feet below. the distance, s, that the acorn is from the ground as it falls is represented by the equation $s(t) = -16t^2 + 25$, where $t$ is the number of seconds. for which interval of time is the acorn moving through the air?○ $0 < t \\leq \\frac{5}{4}$○ $0 < t < \\frac{5}{4}$○ $t > \\frac{5}{4}$○ $-\\frac{5}{4} < t < \\frac{5}{4}$

an acorn falls from the branch of a tree to the ground 25 feet below. the distance, s, that the acorn is from the ground as it falls is represented by the equation $s(t) = -16t^2 + 25$, where $t$ is the number of seconds. for which interval of time is the acorn moving through the air?○ $0 < t \\leq \\frac{5}{4}$○ $0 < t < \\frac{5}{4}$○ $t > \\frac{5}{4}$○ $-\\frac{5}{4} < t < \\frac{5}{4}$

Answer

Explanation:

Step1: Set distance to ground = 0

$S(t) = 0 = -16t^2 + 25$

Step2: Solve for $t^2$

$16t^2 = 25 \implies t^2 = \frac{25}{16}$

Step3: Solve for positive $t$

$t = \sqrt{\frac{25}{16}} = \frac{5}{4}$

Step4: Define valid time interval

Time starts at $t>0$ (when it falls) and ends at $t=\frac{5}{4}$ (when it hits ground, stops moving through air). So $0 < t < \frac{5}{4}$.

Answer:

$0 < t < \frac{5}{4}$