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Annette [7]
3 years ago
14

A model rocket is launched directly upward at a speed of 16 meters per second from a height of 2 meters. The function f(t)=−4.9t

2+16t+2, models the relationship between the height of the rocket and the time after launch, t, in seconds. Which is the maximum height, in meters, the rocket will reach?
Physics
1 answer:
Crank3 years ago
8 0

Answer:

Hmax=15.06 meters

Explanation:The question ask for the maximum value of the function f(t) which can be find by find the maxima of the function

The maxima of the function occurs when the slope is zero. i.e.

\frac{df}{dt} =0\\\frac{df}{dt} =\frac{d}{dt} (-4.9t^2+16t+2)\\\frac{df}{dt} =-4.9*2t+16\\-9.8t+16=0\\t=16/9.8\\t=1.63 secs

Hence the maxima occurs at t=1.63 seconds

The maximum value of f is

f(1.63)=-4.9(1.63^2)+16(1.63)+2\\f(1.63)=15.06\\

hence maximum height is found to be

Hmax=15.06 meters

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Explanation:

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P=\dfrac{1}{3}P_0

\dfrac{1}{3}P_0=P_0e^{-k35000}\\\Rightarrow \dfrac{1}{3}=e^{-k35000}\\\Rightarrow 3=e^{k35000}\\\Rightarrow ln3=k35000\\\Rightarrow k=\dfrac{ln3}{35000}\\\Rightarrow k=3.13\times 10^{-5}

Now

P=\dfrac{1}{2}P_0

ln2=kh\\\Rightarrow h=\dfrac{ln2}{k}\\\Rightarrow h=\dfrac{ln2}{3.13\times 10^{-5}}\\\Rightarrow h=22145.27733\ ft

The altitude will be 22145.27733 ft

P=0.02P_0

0.02P_0=P_0e^{-kh}\\\Rightarrow 0.02=e^{-3.13\times 10^{-5}h}\\\Rightarrow ln0.02=-3.13\times 10^{-5}h\\\Rightarrow h=\dfrac{ln0.02}{-3.13\times 10^{-5}}\\\Rightarrow h=124984.76055\ ft

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The half - life is the time taken for half of a radioactive substance to decay by half.

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           10min             100000                   _

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           30min             25000                    2

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so, the minimum coefficient of static friction must be 0.39.

5 0
3 years ago
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