Anonymous
Anonymous asked in Science & MathematicsMathematics · 8 months ago

# A child's mobile makes one full rotation every 15 seconds. Through what angles has the mobile rotated after 5 minutes? Options are below.?

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• 8 months ago

5 min = 5 * 60 = 300 s

300/15 = 20 rotations

20 rotations * 2pi/rotation = 40pi radians

• 8 months ago

A child's mobile makes one full rotation every 15 seconds.

Through what angles has the mobile rotated after 5 minutes?

The number of 15 seconds in 5 minutes is 20.

• 8 months ago

15 seconds = 1/4 minute

5 minutes = 20 * 15 seconds

so 20 revolutions

• 8 months ago

5 minutes x (60 seconds / 1 minute) = 300 seconds.

300 / 15 = 20 rotations.

20 rotations = 40π radians (c).

• 8 months ago

1 full rotation is 360° or 2π radians.

Intuitively:

In 1/4 minute (15 seconds) --> 2π radians.

In 1 minute --> 8π radians

In 5 minutes --> 40π radians

If you want to be a little more formal:

2π radians / 15 seconds * 60 seconds / minute * 5 minutes

= (2π * 60 * 5) / 15 radians

= 2π * 4 * 5 radians