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3 years ago

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

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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

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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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3 years ago

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

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