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The waterjet's form that spews up from the nozzle is drawn as the parabola. The formula is h= -0,9a^2 + 2,7a. 

 

A. 2,30 metres right of the nozzle Beatrice walks. Her height is 1,50 metres. Will she get wet if she stands there?

B. After what distance does the water come down on the ground again?

C. Chris walks to the exact spot where the water is highest. He is 1,60 metres long. Will he get wet?

Guest Mar 19, 2018

Best Answer 

 #1
avatar+20022 
+2

The waterjet's form that spews up from the nozzle is drawn as the parabola. The formula is h= -0,9a^2 + 2,7a. 

 

A. 2,30 metres right of the nozzle Beatrice walks. Her height is 1,50 metres. Will she get wet if she stands there?

\(\begin{array}{|rcll|} \hline h(a) &=& -0,9a^2 + 2,7a \\ h(2,30) &=& -0,9\cdot 2,30^2 + 2,7\cdot 2,30 \\ h(2,30) &=& 1.449\ \text{metres.} \\ \hline \end{array}\)

She will get wet.

 

B. After what distance does the water come down on the ground again?

\(\begin{array}{|rcll|} \hline h(a) &=& -0,9a^2 + 2,7a \quad &| \quad h(a) = 0 \\ 0 &=& -0,9a^2 + 2,7a \\ a\cdot (-0,9a+2,7) &=& 0 \\\\ -0,9a+2,7 &=& 0 \\ a &=& \frac{2,7}{0,9} \\ a &=& 3 \ \text{metres.} \\ \hline \end{array} \)

After 3 metres does the water come down on the ground again.

 

C. Chris walks to the exact spot where the water is highest. He is 1,60 metres long. Will he get wet?

\(\text{The highest Point at $\dfrac{3 \ \text{metres.}}{2} = 1,5 $ metres. }\)

\(\begin{array}{|rcll|} \hline h(1,5) &=& -0,9\cdot 1,5^2 + 2,7\cdot 1,5 \\ h(1,5) &=& 2,025\ \text{metres.} \\ \hline \end{array}\)

He will not get wet.

 

 

laugh

heureka  Mar 19, 2018
 #1
avatar+20022 
+2
Best Answer

The waterjet's form that spews up from the nozzle is drawn as the parabola. The formula is h= -0,9a^2 + 2,7a. 

 

A. 2,30 metres right of the nozzle Beatrice walks. Her height is 1,50 metres. Will she get wet if she stands there?

\(\begin{array}{|rcll|} \hline h(a) &=& -0,9a^2 + 2,7a \\ h(2,30) &=& -0,9\cdot 2,30^2 + 2,7\cdot 2,30 \\ h(2,30) &=& 1.449\ \text{metres.} \\ \hline \end{array}\)

She will get wet.

 

B. After what distance does the water come down on the ground again?

\(\begin{array}{|rcll|} \hline h(a) &=& -0,9a^2 + 2,7a \quad &| \quad h(a) = 0 \\ 0 &=& -0,9a^2 + 2,7a \\ a\cdot (-0,9a+2,7) &=& 0 \\\\ -0,9a+2,7 &=& 0 \\ a &=& \frac{2,7}{0,9} \\ a &=& 3 \ \text{metres.} \\ \hline \end{array} \)

After 3 metres does the water come down on the ground again.

 

C. Chris walks to the exact spot where the water is highest. He is 1,60 metres long. Will he get wet?

\(\text{The highest Point at $\dfrac{3 \ \text{metres.}}{2} = 1,5 $ metres. }\)

\(\begin{array}{|rcll|} \hline h(1,5) &=& -0,9\cdot 1,5^2 + 2,7\cdot 1,5 \\ h(1,5) &=& 2,025\ \text{metres.} \\ \hline \end{array}\)

He will not get wet.

 

 

laugh

heureka  Mar 19, 2018

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