A 20 kg truck drives in a circle of radius 4 m at 10m/s. What is the
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Answer:
Speed of the point = 1.541 × 10⁶ m/h = 428 m/s
Explanation:
Modelling the earth as a sphere,
The equator and the pole have a length of an arc that's fully 90° of the whole 360° circular circumference.
A point located 1/4 of the length of the arc between the equator and the pole has an angle (1/4) × 90° arc = 22.5°.
On the attached image, θ = 22.5°, so Φ = 90° - 22.5° = 67.5°
To obtain the radius of the point on the globe
From the image again, it shows that trigonometric relations can be used to obtain this radius
Sin Φ = (radius of the point)/(radius of the earth)
Sin 67.5 = radius of the point/(6.37 × 10⁶)
Radius of the point = 6.37 × 10⁶ × 0.9239 = 5.885 × 10⁶ m
Speed of the point on the globe = (circumference of the circular path mapped out by the point during rotation)/(24 hours)
circumference of the circular path mapped out by the point during rotation = 2πr = 2π × 5.885 × 10⁶ = 3.6977 × 10⁷ m
Speed of the point = 3.6977 × 10⁷/24 = 1.541 × 10⁶ m/h = 428 m/s
