Question

neglecting air resistance, the distance s(t) in feet traveled by a freely - falling object is given by the function s(t)=16t², where t is time in seconds. the height of a certain tower is 953 feet. how long would it take an object to fall to the ground from the top of the building? seconds (round to two decimal places as needed.)

Explanation:

Step1: Set up the equation

We know that the distance formula is $s(t)=16t^{2}$, and the height of the tower (distance the object needs to fall) is 953 feet. So we set $s(t) = 953$, giving the equation $16t^{2}=953$.

Step2: Solve for $t^{2}$

Divide both sides of the equation $16t^{2}=953$ by 16. We get $t^{2}=\frac{953}{16}=59.5625$.

Step3: Solve for $t$

Take the square - root of both sides. Since $t$ represents time and cannot be negative in this context, $t=\sqrt{59.5625}$.

Step4: Calculate the value of $t$

$t\approx7.72$ seconds.

Answer:

7.72 seconds