HELP PLEASE! The distance d that an object falls is directly proportional to the square of the time of the fall,t. A person who is parachuting for the first time is told to wait 12 seconds before opening the parachute. If the person falls 64 feet in 2 seconds, find how far he falls in 12 seconds.
distance is ___ feet
since distance is proportional to t^2, then since 12 = 6*2, the distance fallen in 12 seconds will be 36 times the distance fallen in 2 seconds.
To solve this problem, we need to use the given information that the distance an object falls is directly proportional to the square of the time of the fall, t.
Let's first find the constant of proportionality, k, by using the information that the person falls 64 feet in 2 seconds.
d = kt^2
64 = k(2^2)
64 = 4k
To find k, divide both sides of the equation by 4:
k = 16
Now that we have the value of k, we can find the distance the person falls in 12 seconds by substituting t = 12 into the equation:
d = kt^2
d = 16(12^2)
d = 16(144)
d = 2,304
Therefore, the person falls 2,304 feet in 12 seconds.
To solve this problem, we need to use the information given that distance (d) is directly proportional to the square of the time (t).
We know that the person falls 64 feet in 2 seconds. Let's assign these values to the variables d1 and t1:
d1 = 64 feet
t1 = 2 seconds
We can use this information to find the constant of proportionality (k) in the equation d = kt². Rearranging the equation, we get k = d/t².
Now, let's find the value of k using the given information:
k = d1 / t1²
k = 64 feet / (2 seconds)²
k = 64 feet / 4 seconds²
k = 64/4
k = 16
We have determined that k is equal to 16.
Now we can use the equation d = kt² and substitute the value of k to find the distance (d) when the time (t) is 12 seconds:
d = 16 * 12²
d = 16 * 144
d = 2,304 feet
Therefore, the person falls 2,304 feet in 12 seconds.