Mathematics: In a free-fall experiment, an object is dropped from a height of h = 400 feet. a camera on the ground 500 ft from the point of impact records the fall of the object (the shape is a 90 degree angle with 500 ft at the bottom). (a) find the position function that yields the height of the object at time t assuming the object is released at time t = 0. h(t) = at what time will the object reach ground level? (round your answer to three decimal places.) t = 5.12 sec (b) find the rates of change of the

In a free-fall experiment, an object is dropped from

Ответ:

texas101st78

02.01.2022

Hmmm the object, is at rest, when dropped, so it has a velocity of 0 ft/s

the only force acting on the object, is gravity, using feet will then be -32ft/s²,

was wondering myself on -32 or 32.. but anyhow... we'll settle for the negative value, since it seems to be just a bit of convention issues

so, we'll do the integral to get v(t) then

$\bf \displaystyle \int -32\cdot dt\implies -32t+C
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\textit{object moves from \underline{rest}, so velocity is 0 at 0secs}
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-32(0)+C=0\implies C=0\implies \boxed{v(t)=-32t}
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\textit{now to get the positional s(t)}
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\displaystyle \int -32t\cdot dt\implies -16t^2+C
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\textit{the initial \underline{position} was 400ft away at 0secs}
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-16(0)^2+C=400\implies C=400\implies \boxed{s(t)=-16t^2+400}$

when will it reach the ground level? let's set s(t) = 0

$\bf s(t)=-16t^2+400\implies 0=-16t^2+400\implies \cfrac{-400}{-16}=t^2
\\\\\\
25=t^2\implies \boxed{5=t}$

part B) check the picture below

In a free-fall experiment, an object is dropped from a height of h = 400 feet. a camera on the groun

In a free-fall experiment, an object is dropped from a height of h = 400 feet. a camera on the groun

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Ответ:

christianskyy7074

22.12.2021

Mathematics

IS THIS WHO I THINK IT I

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