Questions: The formula s=16 t^2 is used to approximate the distance s, in feet, that an object falls freely from rest in t seconds. The height of a building is 1213 feet. How long would it take for an object to fall from the top? The object would fall for seconds. (Simplify your answer. Type an integer or a decimal rounded to the nearest thousandth.)

The formula s=16 t^2 is used to approximate the distance s, in feet, that an object falls freely from rest in t seconds. The height of a building is 1213 feet. How long would it take for an object to fall from the top?

The object would fall for seconds.

(Simplify your answer. Type an integer or a decimal rounded to the nearest thousandth.)

Transcript text: The formula $s=16 t^{2}$ is used to approximate the distance $s$, in feet, that an object falls freely from rest in $t$ seconds. The height of a building is 1213 feet. How long would it take for an object to fall from the top? The object would fall for $\square$ seconds. (Simplify your answer. Type an integer or a decimal rounded to the nearest thousandth.)

Solution

Solution Steps

Step 1: Identify the given information

We are given the formula for the distance $ s $ that an object falls freely from rest: \[ s = 16t^2 \] We are also given the height of the building: \[ s = 1213 \text{ feet} \]

Step 2: Set up the equation

We need to find the time $ t $ it takes for the object to fall 1213 feet. Substitute $ s = 1213 $ into the formula: \[ 1213 = 16t^2 \]

Step 3: Solve for $ t $

First, isolate $ t^2 $ by dividing both sides of the equation by 16: \[ t^2 = \frac{1213}{16} \] \[ t^2 = 75.8125 \]

Next, take the square root of both sides to solve for $ t $: \[ t = \sqrt{75.8125} \] \[ t \approx 8.7059 \]