the distance, d, an object falls when dropped from a tower varies directly as the square of the time it falls. If the object falls 144 feet in 3 seconds, how far will it fall in 11 seconds?
Consider the condition:
"varies directly as the square of the time it falls"
Which one do you think applies:
a. 144*(3/11)²
b. 144*(11/3)
c. 144*(3/11)
d. 144*(11/3)²
To solve this problem, we can use the concept of direct variation, which states that if two quantities are directly proportional, their ratio will remain constant. In this case, the distance an object falls is directly proportional to the square of the time it falls.
Let's denote the distance as d and the time as t. Then we can establish the following equation:
d = kt^2
where k is the constant of variation. We need to find the value of k first before we can determine the distance in 11 seconds.
Given that the object falls 144 feet in 3 seconds, we can substitute these values into the equation:
144 = k * 3^2
144 = k * 9
To solve for k, we divide both sides of the equation by 9:
k = 144 / 9
k = 16
Now that we know the value of k, we can substitute it back into the equation and solve for the distance in 11 seconds:
d = 16 * 11^2
d = 16 * 121
d = 1936
Therefore, the object will fall 1936 feet in 11 seconds.