To determine the height [tex]\( h \)[/tex] of the concrete block above the ground after [tex]\( s \)[/tex] seconds, we need to understand how the height changes over time.
1. Starting Height:
The block starts at a height of 270 feet.
2. Rate of Descent:
The block descends at a constant rate of 2.5 feet per second.
3. Time Elapsed:
Let [tex]\( s \)[/tex] represent the number of seconds that have passed.
Given these points, we need an expression for [tex]\( h \)[/tex] that considers how the height decreases over time.
Initially, at [tex]\( s = 0 \)[/tex], the block is at 270 feet. After [tex]\( s \)[/tex] seconds, the height decreases due to the descent of 2.5 feet per second. Therefore, the total descent after [tex]\( s \)[/tex] seconds is [tex]\( 2.5s \)[/tex] feet.
To find the remaining height [tex]\( h \)[/tex] above the ground after [tex]\( s \)[/tex] seconds, we subtract the total descent from the initial height:
[tex]\[ h = 270 - 2.5s \][/tex]
This equation accounts for the initial height of 270 feet and reduces the height by 2.5 feet for every second that passes.
Among the given choices:
- (A) [tex]\( h = 270s + 2.5 \)[/tex] is incorrect because it suggests an increasing height starting from zero.
- (B) [tex]\( h = 2.5s + 270 \)[/tex] is incorrect for similar reasons; it incorrectly represents the height increasing over time.
- (C) [tex]\( h = 270 - 2.5s \)[/tex] is correct as it appropriately models the descent from an initial 270 feet.
- (D) [tex]\( h = 2.5s - 270 \)[/tex] is incorrect because it suggests a potentially negative height starting from a large negative value.
Therefore, the correct function to determine [tex]\( h \)[/tex], the height in feet above the ground of the concrete block after [tex]\( s \)[/tex] seconds, is:
[tex]\[ \boxed{C: \ h = 270 - 2.5s} \][/tex]
