If the circumference of a circle is 47.7, what is the area of the circle

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

2 years ago

A bag contains 7 marbles, of which I is orange,

lyudmila [28]

6/7 because only one marble is orange

5 0

3 years ago

HjkkjikmjikiikigyjkbvcfAAAWFKO

kobusy [5.1K]

1. 3 & 7 and 2 & 6

2. 5

3. Alternate exterior angles

4. Consecutive interior angles

5. 2

6. 4

7. 146

8. 128

9. 13x + 63 = 180
13x = 117
x = 9

8x + 63 = y
8(9) + 63 = y
72 + 63 = y

m
10. 5x = m5(9) = 45

m
11. 2 & 7 and 1 & 8

12. 8

13. Alternate interior angles

5 0

3 years ago

What fraction is greater than 0.7 but less than 0.71

alexgriva [62]

Are there any answer choices because this question has multiple answers.

4 0

3 years ago

Which statement describes a unit rate? Group of answer choices Sara is reading 97 words in 1 minute. Sara ate 3 crackers and 1 a

castortr0y [4]

Answer:

97 words in 1 minute

Step-by-step explanation:

A unit measure is so many somethings done usually per unit time. Examples

1 orange in 1 minute.
10 tomatoes per tomato plant
50 miles in one hour
10 cookies per week

3 crackers and 1 apple is not. For ever apple, she ate 3 crackers would be

1 cookie is not. It is not per anything.

Driving 16 miles is not. Again, it is not per anything.

The answer is 97 words in 1 minute.

6 0

3 years ago