Question

An entomologist discovers a dung beetle rolling a ball of dung along the ground, and decides to follow it.

1. (a) The beetle initially moves 580 cm to the east, before continuing north-east for 150 cm. At this point, the beetle becomes aware of the researcher following it, and attempts to flee to the south. It only makes it 45 cm, however, before the entomologist collects the ball of dung for further experiments.

   1. i) Draw a diagram of the dung beetle’s path, breaking segments into components if required.

   2. ii) Using the correct SI unit and significant figures, calculate

      1. A) the distance the beetle travelled, and

      2. B) the magnitude of the beetle’s displacement (i.e. the distance from its initial position) when its ball of dung was taken.

2. (b) The entomologist wishes to determine size of the ball of dung, and measures its radius to be 3.18 cm. Use scientific notation to write the volume of the ball in units of cubic metres.

Answer 1

(a)

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(b) distance traveled is just the sum

d = 580 + 150 + 45

d = 775 cm or 7.75 m (distance traveled)

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(c) d_x = 580 + 150cos45 = 686.1 cm

d_y = 150sin45 - 45 = 61.1 cm

so,

d = sqrt ( 686.1² + 61.1²)

d = 688.8 cm or 6.888 m ( displacement)

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(d) Volume of sphere = (4/3) * pi * r³

Volume = (4/3) * pi * 0.0318³

Volume = 1.35e-4 m³