The function would be h = 270 - 2.5s, where h is the height (in feet) and s it the time (in seconds) that has passed.
The 270 represents the initial value, which is given. We are told that the initial height of the block is 270 feet.
2.5s represents the feet that it has descended. We know the block is lowered at a rate of 2.5 feet per second. Multiplying this by s, the time, will give us how much it has descended.
The height at any point is can be given by function f(s) = 270 - 2.5s.
Given to us,
concrete block top height, H = 270 feet,
speed of the block, v = 2.5 feet/second,
We know that [tex]\rm \bold{speed = \dfrac{Distance}{Time} }[/tex],
thus, [tex]\rm \bold{Distance = speed\times Time}[/tex]
So, we can write, height (distance from the top height) covered is "s" seconds as,
[tex]\bold{h = v \times s}=\bold{2.5\times s} = \rm \bold{2.5s}[/tex]
therefore, we can write,
Height at any point = Top height - height covered
= 270 - 2.5s
Hence, the height at any point is can be given by function f(s) = 270 - 2.5s.
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