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35 votes
35 votes
a field mouse has been doing some parkour training after implementing a new workout program he can now jump along a parabolic path given byf(x)=-.2x^2+1.6x a) how far can the mouse jump horizontally (round to the nearest ft)?b) with his new workout program can the mouse jump over 3 ft fence

User Nekketsuuu
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1 Answer

21 votes
21 votes

a.

Given the equation of the jumps as;


f(x)=-0.2x^2+1.6x

We want to find the range of the jump.To do this let us substitute f(x) = 0 and solve for x;


\begin{gathered} f(x)=-0.2x^2+1.6x=0 \\ -0.2x^2+1.6x=0 \\ -0.2x^2=-1.6x \\ \text{divide both sides by -0.2x} \\ (-0.2x)/(-0.2x)^2=(-1.6x)/(-0.2x) \\ x=8\text{ ft} \end{gathered}

Therefore, the mouse can jump 8 ft horizontally.

b.

We want to know if the mouse can jump over a 3ft fence;

Let's substitute x=8/2 =4 into the equation to get the maximum height the mouse can reach;


\begin{gathered} f(x)=-0.2x^2+1.6x \\ f(4)=-0.2(4)^2+1.6(4) \\ f(4)=3.2ft \end{gathered}

since the maximum height is more than 3ft, it means the mouse can jump higher than 3 ft.

since the maximum height the mouse can jump is 3.2ft, and the fence is 3 ft, the difference between the maximum height and the height of the fence is;


\begin{gathered} 3.2ft-3.0ft \\ =0.2ft \end{gathered}

So, the mouse can jump 0.2ft higher than the 3ft fence.

Therefore, the mouse can clear it with 0.2 ft.


\text{Yes, the mouse can clear it by 0.2ft}

User Aditya Talpade
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