The distance 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 15 seconds before opening the parachute. If the person falls 64 feet in 2 seconds, find how far he falls in 15 seconds
d = k t^2
64 = k (2)^2
so
k = 64/4 = 16
then
d = 16 (15)^2
d = 16 * 225
d = 3600 feet
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check
g = 32 ft/s^2
h = (1/2) g t^2 = 16 t^2
yes
To solve this problem, we can use the formula for distance fallen:
distance = k * (time)^2
where k is the constant of proportionality. We need to find the value of k.
Given that the person falls 64 feet in 2 seconds, we can substitute these values into the formula:
64 = k * (2)^2
Simplifying the equation:
64 = 4k
Dividing both sides by 4:
k = 16
Now that we have the value of k, we can find the distance fallen in 15 seconds:
distance = 16 * (15)^2
Simplifying the equation:
distance = 16 * 225
distance = 3600 feet
Therefore, the person falls 3600 feet in 15 seconds.
To solve the problem, we can use the formula for distance fallen:
d = kt^2
where d is the distance fallen, k is the constant of proportionality, and t is the time of the fall.
We are given the distance fallen (d = 64 feet) and the time of the fall (t = 2 seconds). We can use these values to find the value of the constant of proportionality, k.
64 = k * 2^2
64 = 4k
Dividing both sides by 4:
k = 16
Now that we have the value of k, we can use it to find the distance fallen in 15 seconds:
d = 16 * 15^2
d = 16 * 225
d = 3600 feet
Therefore, the person falls 3600 feet in 15 seconds.