The distance d that and 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 19 seconds before opening the parachute. If the person falls 64 feet in 2 seconds, find how far he falls in 19 seconds.

Question

sasogeek · Answer

when something, say x is directly proportional to something else, say y, it means that if x increases, y also increases but by a certain factor which we call a constant, or a constant of proportionality usually represented by the letter k. hence x = ky

in this case, we're told that d is proportional to the square of t, which means that d will increase by a factor of increase in the square of t. mathematically you will write that as
d = k(t)^2

In 2 seconds, this person falls 64 feet. using our equation, we can find the constant of proportionality to know the factor that d increases by as t increases.
d = k (t)^2                  d=64,  t=2
64=k(2)^2
64=4k
64/4 = k
16 = k
=> k = 16

this means that we can now find how far the person would have fallen after 19 seconds...
d = 16 (t)^2

you know the value of t now, you know the value of the constant k too,  can you find d?

anonymous · Answer

The distance is ? feet. is that what i need to solve for?

sasogeek · Answer

solve for d, and add feet to the figure u get as ur answer :)

anonymous · Answer

So i solve for d with the equation you gave m?

sasogeek · Answer

yes, but do you even understand what those equations mean?

anonymous · Answer

sorta im a little confused sorry

sasogeek · Answer

its ok :) i'll explain... you're treating variations... right?