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2 years ago

Explain why the scale from ABC to DEF could be 1:3

Mathematics

1 answer:

BlackZzzverrR [31]2 years ago

8 0

Answer:

Don't really know

Step-by-step explanation:

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In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 3.0 m/s up a 22.0° inclined track

Aloiza [94]

Answer:

Approximately $0.31\; \rm m$ , assuming that $g = 9.81\; \rm N \cdot kg^{-1}$ .

Step-by-step explanation:

Initial kinetic energy of the sled and its passenger:

$\begin{aligned}\text{KE} &= \frac{1}{2}\, m \cdot v^{2} \\ &= \frac{1}{2} \times 14\; \rm kg \times (3.0\; \rm m\cdot s^{-1})^{2} \\ &= 63\; \rm J\end{aligned}$ .

Weight of the slide:

$\begin{aligned}W &= m \cdot g \\ &= 14\; \rm kg \times 9.81\; \rm N \cdot kg^{-1} \\ &\approx 137\; \rm N\end{aligned}$ .

Normal force between the sled and the slope:

$\begin{aligned}F_{\rm N} &= W\cdot \cos(22^{\circ}) \\ &\approx 137\; \rm N \times \cos(22^{\circ}) \\ &\approx 127\; \rm N\end{aligned}$ .

Calculate the kinetic friction between the sled and the slope:

$\begin{aligned} f &= \mu_{k} \cdot F_{\rm N} \\ &\approx 0.20\times 127\; \rm N \\ &\approx 25.5\; \rm N\end{aligned}$ .

Assume that the sled and its passenger has reached a height of $h$ meters relative to the base of the slope.

Gain in gravitational potential energy:

$\begin{aligned}\text{GPE} &= m \cdot g \cdot (h\; {\rm m}) \\ &\approx 14\; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \times h\; {\rm m} \\ & \approx (137\, h)\; {\rm J} \end{aligned}$ .

Distance travelled along the slope:

$\begin{aligned}x &= \frac{h}{\sin(22^{\circ})} \\ &\approx \frac{h\; \rm m}{0.375}\end{aligned}$ .

The energy lost to friction (same as the opposite of the amount of work that friction did on this sled) would be:

$\begin{aligned} & - (-x)\, f \\ = \; & x \cdot f \\ \approx \; & \frac{h\; {\rm m}}{0.375}\times 25.5\; {\rm N} \\ \approx\; & (68.1\, h)\; {\rm J}\end{aligned}$ .

In other words, the sled and its passenger would have lost (approximately) $((137 + 68.1)\, h)\; {\rm J}$ of energy when it is at a height of $h\; {\rm m}$ .

The initial amount of energy that the sled and its passenger possessed was $\text{KE} = 63\; {\rm J}$ . All that much energy would have been converted when the sled is at its maximum height. Therefore, when $h\; {\rm m}$ is the maximum height of the sled, the following equation would hold.

$((137 + 68.1)\, h)\; {\rm J} = 63\; {\rm J}$ .

Solve for $h$ :

$(137 + 68.1)\, h = 63$ .

$\begin{aligned} h &= \frac{63}{137 + 68.1} \approx 0.31\; \rm m\end{aligned}$ .

Therefore, the maximum height that this sled would reach would be approximately $0.31\; \rm m$ .

7 0

3 years ago

What does x equal? 2x-8=2x+6+x

Charra [1.4K]

2x-8=2x+6+x first put all the like terms together
2x-8=3x+6 subtract 2s from both sides
-8=x+6 subtract 6 from both sides
-14=x then it is your final answer!

Hope this helps! Please give me the brainliest answer if you like it! If you have further questions, please leave a comment or add me as a friend!

7 0

3 years ago

Read 2 more answers

On Monday Ravi drives for 4 hours.

tensa zangetsu [6.8K]

Answer:

Step-by-step explanation:

On Monday Ravi drives for 4 hours.

His average speed is 30 mph.

How far does Ravi drive on Monday?

4 0

3 years ago

Read 2 more answers

Each of 5 birdwatchers reported seeing 15 roseate spoonbills in a day. If they each reported seeing the same nunber of roseate s

LuckyWell [14K]

Each of the 5 saw 15 birds a day, so they saw 75 each day for 14 days. 75 times 14 is 1,050. They saw in total, 1,050 birds.

4 0

4 years ago

Express 4 4/9 as an improper fraction. Example please.

miskamm [114]

Simple...

you have: $4 \frac{4}{9}$

To make this into an improper fraction-->>

1.) Multiply whole number by denominator

2.)Add the number you got plus the numerator

3.) Use the original denominator to finish your improper fraction

Example: $4\frac{4}{9}$

4*9=36

36+4=40

$\frac{40}{9}$

Thus, your answer.

3 0

3 years ago