Use the given information to answer the question.
The distance $s$ that an object falls varies directly with the square of the time, $t$, of the fall. If an object falls 16 feet in one second, how long will it take for it to fall 80 feet?
Round your answer to two decimal places.
It will take Number seconds for the object to fall 80 feet.
Answer
Round the answer to two decimal places: $t \approx \boxed{2.24}$.
Step 1 ：Since the distance $s$ varies directly with the square of the time $t$, we can write the equation as $s = kt^2$, where $k$ is a constant.
Step 2 ：Given that an object falls 16 feet in one second, we can plug in the values to find the constant $k$: $16 = k(1)^2$, so $k = 16$.
Step 3 ：Now we have the equation $s = 16t^2$.
Step 4 ：To find the time it takes for the object to fall 80 feet, we set $s$ to 80: $80 = 16t^2$.
Step 5 ：Divide both sides by 16: $5 = t^2$.
Step 6 ：Take the square root of both sides: $t = \sqrt{5}$.
Step 7 ：Round the answer to two decimal places: $t \approx \boxed{2.24}$.
