The distance, d, that an object falls is directly proportional to the square of the time, t, it has been in free fall. An object that has been in free fall for 3 seconds has fallen 144 feet. Determine the distance the object has fallen if it has been falling for 4 seconds.
d = ? ft
We can set up a proportion to solve this problem.
Since the distance, d, is directly proportional to the square of the time, t, we can write the proportion as:
d₁/t₁² = d₂/t₂²
where d₁ is the distance the object has fallen in t₁ seconds, and d₂ is the distance we want to find in t₂ seconds.
We are given that the object has fallen 144 feet in 3 seconds, so we have:
144/3² = d₂/4²
Simplifying, we get:
144/9 = d₂/16
Cross multiplying, we have:
9 * d₂ = 144 * 16
Solving for d₂, we get:
9 * d₂ = 2304
d₂ = 2304/9 ≈ 256
Therefore, if the object has been falling for 4 seconds, it would have fallen approximately 256 feet.
To solve this problem, we can first write the equation that represents the given information:
d = kt^2
where d is the distance fallen, t is the time in seconds, and k is the proportionality constant.
Using the given information, we can substitute the values:
144 = k * 3^2
Simplifying this equation:
144 = k * 9
Now, to find the value of k, we divide both sides of the equation by 9:
k = 144 / 9
k = 16
So, the equation becomes:
d = 16t^2
Now, we can substitute the value of t = 4 seconds into the equation to find the distance fallen:
d = 16 * 4^2
d = 16 * 16
d = 256 feet
Therefore, if the object has been falling for 4 seconds, it will have fallen 256 feet.
To solve this problem, we can use the concept of direct variation. Direct variation states that when two variables, in this case distance (d) and the square of time (t^2), are directly proportional, their relation can be represented by an equation of the form d = kt^2, where k is the constant of proportionality.
We are given that an object falling for 3 seconds has fallen 144 feet. So we can substitute these values into the equation to find k.
144 = k * 3^2
144 = k * 9
k = 144/9
k = 16
Now that we know the value of k, we can use it to find the distance the object has fallen after 4 seconds.
d = 16 * 4^2
d = 16 * 16
d = 256 feet
Therefore, if the object has been falling for 4 seconds, it would have fallen 256 feet.