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A train is running on a circular track of radius 1 km at the r

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A train is running on a circular track of radius 1 km at the rate of 36 km per hour. Find the angle, to the nearest minute, through which it will turn in 30 seconds.

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A train is running on a circular track of radius 1 km at the rate of 36 km per hour. Find the angle, to the nearest minute, through which it will turn in 30 seconds.

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Text solutionVerified

Radius of circular track

= r = 1 km

Circumference

= 2 π r = 2 πkm

Speed of train

= 36

km\hr

Distance moved by train in 30 seconds

= 36 \times \frac{30}{3600}

= \frac{3}{10}

For

2 π

km, train turns

2 π^{c}

∴

For

\frac{3}{10}

km, train turns

\frac{3}{10}^{c} = \frac{54}{π}^{\circ}

1 minute of arc

= \frac{1}{60}^{\circ}

Angle turned by train

= (\frac{54 \times 60}{π})

minutes of arc.

≃ 1031

minutes

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Question Text	A train is running on a circular track of radius 1 km at the rate of 36 km per hour. Find the angle, to the nearest minute, through which it will turn in 30 seconds.
Answer Type	Text solution:1
Upvotes	150

A train is running on a circular track of radius 1 km at the rate of 36 km per hour. Find the angle, to the nearest minute, through which it will turn in 30 seconds.

Text solutionVerified

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