This has me stumped
The approximate time in seconds, that it takes an object to fall d feet under the influence of gravity is given by mathematical model t=square root d/16. A rock dropped from a cliff hits the ground 6 seconds later. How high is the cliff?
or rearranged
distance fallen = 16 t^2
so if t=6
dist = 16(36) = 576
so the cliff is 576 feet high
To find the height of the cliff, we can use the given mathematical model:
t = √(d/16)
We are given that the time it takes for the rock to hit the ground is 6 seconds. Let's substitute this value into the equation:
6 = √(d/16)
To solve for d (the height of the cliff), we need to isolate it by squaring both sides of the equation:
(6)^2 = (√(d/16))^2
36 = d/16
Now, we can solve for d by multiplying both sides of the equation by 16:
36 × 16 = d
576 = d
So, the height of the cliff is 576 feet.