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Triss [41]
3 years ago
9

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 i

mpact records the fall of the object (t
he 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 angle of elevation of the camera when t = 1 and t = 2. (Round your answers to four decimal places.)
θ'(1) =
rad/sec
θ'(2) =
rad/sec

Mathematics
1 answer:
PilotLPTM [1.2K]3 years ago
5 0
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
\\\\\\
\textit{object moves from \underline{rest}, so velocity is 0 at 0secs}
\\\\\\
-32(0)+C=0\implies C=0\implies \boxed{v(t)=-32t}
\\\\\\
\textit{now to get the positional s(t)}
\\\\\\
\displaystyle \int -32t\cdot dt\implies -16t^2+C
\\\\\\
\textit{the initial \underline{position} was 400ft away at 0secs}
\\\\\\
-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

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