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dalvyx [7]
3 years ago
9

A circular track has an inside cirumference of 220m. If the width of track is 3.5m, find its outer circumference.​

Physics
1 answer:
mars1129 [50]3 years ago
8 0

Answer:

Lc = 242 [m]

Explanation:

The circumference is defined as the circumference length of a circle, this length can be calculated by means of the following equation.

L_{c}=2*\pi *r

where:

Lc = circumference length = 220 [m]

r = radius [m]

Now we can clear r

r=\frac{L_{c}}{2*\pi } \\\\r = \frac{220}{2*\pi }\\\\r = 35.01 [m]

Now we can determine the outer radius with the inner diameter plus the width of the track.

R = r + 3.5

R = 35.01 + 3.5 = 38.51 [m]

The outer circumference is:

L_{c} = 2*\pi *38.51 \\L_{c} = 242 [m]

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The graph below shows the position of an ant as it crawls over a flat picnic blanket. The total time for the ant to go from the
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The average speed of the ant is 0.276 cm/s and the average velocity is 0.136 cm/s.

The correct answer is option D.

In the given graph, we can deduce the following;

  • the total time of the motion, = 1 mins + 45 s = 60 s + 45 s = 105 s

The average speed of the ant is calculated as;

average \ speed = \frac{total \ distance }{total \ time }

The total distance from the graph is calculated as follows;

  • first horizontal distance from 2 cm to 8 cm = 8 - 2 = 6 cm
  • first upward distance from 3 cm to 5 cm = 5 - 3 = 2 cm
  • second horizontal distance from 8 cm to 6 cm = 8 - 6 = 2 cm
  • second upward distance from 5 cm to 12 cm = 12 - 5 = 7 cm
  • third horizontal distance from 6 cm to 13 cm = 13 - 6 = 7 cm
  • fourth downward distance from 12 cm to 9 cm = 3 cm
  • final horizontal distance from 13 cm to 15 cm = 2cm

The total distance = (6 + 2 + 2 + 7 + 7 + 3 + 2) cm = 29 cm

average \ speed = \frac{total \ distance }{total \ time } = \frac{29 \ cm}{105 \ s} = 0.276 \ cm/s

The average velocity is calculated as the change in displacement per change in time.

The displacement is the shortest distance between the start and end positions.

  • This shortest distance is the straight line connecting the start and end position. Call this line P
  • From the end position at x = 15 cm, draw a vertical line from y = 9 cm, to y = 3 cm. The displacement = 9 cm - 3 cm = 6 cm
  • Also, draw a horizontal line from start at x = 2 cm to x = 15 cm. The displacement = 15 cm - 2 cm = 13 cm

Notice, you have a right triangle, now calculate the length of  line P.

                                                ↓end

                                                ↓

                                                ↓ 6cm

                                                ↓

  start -------------13 cm------------

Use Pythagoras theorem to solve for P.

P^2 = 6^2 + 13^2\\\\P^2 = 36 + 169\\\\P^2 = 205\\\\P= \sqrt{205} \\\\P = 14.318 \ cm

The average velocity of the ant is calculated as;

average \ velocity= \frac{\Delta displacemnt  }{total\ time }= \frac{14.318 \ cm}{105 \  s} = 0.136 \ cm/s  \\\\

Thus, the average speed of the ant is 0.276 cm/s and the average velocity is 0.136 cm/s.

Learn more here: brainly.com/question/589950

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