Question

question 19, 2.5.25
part 1 of 2
the distance s that an object falls is directly proportional to the square of the time t of the fall. if an object falls 16 feet in 1 second, how far will it fall in 3 seconds? how long will it take an object to fall 400 feet?
an object will fall
feet
seconds in 3 seconds.

Explanation:

Step1: Find the proportionality constant

Since $s$ is directly proportional to $t^{2}$, we have $s = kt^{2}$. Given that $s = 16$ when $t = 1$, substituting these values into the equation gives $16=k\times1^{2}$, so $k = 16$.

Step2: Calculate the distance in 3 seconds

Now that $k = 16$, when $t = 3$, we use the formula $s=kt^{2}$. Substitute $k = 16$ and $t = 3$ into it: $s=16\times3^{2}=16\times9 = 144$.

Answer:

144