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# Help needed

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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

#1
+19207
+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.

heureka  Mar 19, 2018
Sort:

#1
+19207
+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.

heureka  Mar 19, 2018

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