Question

question 19, 2.5.25 part 2 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 144 feet in 3 seconds. it takes for an object to fall 400 feet.

Explanation:

Step1: Establish the proportionality equation

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 $k = 16$. The equation is $s = 16t^{2}$.

Step2: Find the time when $s = 400$

Substitute $s = 400$ into $s = 16t^{2}$, we get $400=16t^{2}$. Then $t^{2}=\frac{400}{16}=25$. Taking the square - root of both sides, since $t>0$ (time cannot be negative in this context), $t = 5$.

Answer:

5 seconds