Clay Vase

Need help with some trigonmetry circle problems?

To make a clay vase, an artist uses a potter's wheel hat has a diameter of 13in. and spins at 120rpm. Find the approximate distance traveled in 1min by a point on the outer edge of the wheel.

Formula s = radius x (angle in radians), r = 13 , angle in radians = 120 x 2pi
Distance s = 13 x 120 x 2pi = 3776.19 inches Is this correct?

A ship is approaching a lighthouse known to be 20m high. The apparent size of the lighthouse is 0.005 radians. Ten minutes later the lighthouse has an apparent size of 0.010 radians. What is the approximate speed of the ship (in km/h)?

➊ C = 2πr = πd

Wheel has DIAMETER of 13" (not RADIUS of 13")

∴ one rev = π(13) = 13π inches

when wheel makes 120 rev, point on outer edge will travel ...

= 120 rev x (13π inches /rev) = 1560π inches = 4900.884 ... = 4901 inches

➋ at greater distance R, arc length 20 m = R•θ = R(0.005)

∴ R = 20 ÷ 0.005 = 4000 m

at lesser distance r, arc length 20 m = r•θ = R(0.010)

∴ r = 20 ÷ 0.010 = 2000 m

The ship has become 4000 – 2000 = 2000 m = 2 km closer in the 10 minute (= ⅙ hour) interval of time

∴ ship's speed = distance ÷ time = 2 km ÷ (⅙ h) = 12 km/h

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