Question

A flea hops in a straight path along a meter stick, starting at 0.7 cm and making successive jumps, which are measured to be 3.2 cm, 6.5 cm, 8.3 cm, 10.0 cm, 11.5 cm, and 15.5 cm. Express the answers to the following questions in scientific notation, with units of meters and an appropriate number of significant figures. What is the total distance covered by the flea in these six hops? What is the average distance covered by the flea in a single hop?

Answer 1

Answer on Question #74108, Physics / Mechanics | Relativity

A flea hops in a straight path along a meter stick, starting at 0.7 cm and making successive jumps, which are measured to be 3.2 cm, 6.5 cm, 8.3 cm, 10.0 cm, 11.5 cm, and 15.5 cm. Express the answers to the following questions in scientific notation, with units of meters and an appropriate number of significant figures.

What is the total distance covered by the flea in these six hops?

What is the average distance covered by the flea in a single hop?

Solution:

The total distance is

$$d = x_f - x_i = (15.5 - 0.7) = 14.8 \text{ cm} = 1.48 \times 10^{-1} \text{ m}.$$

where $x_i$ is initial coordinate and $x_f$ is final coordinate.

The average distance covered by the flea in a single hop is

$$d_{avg} = \frac{d_1 + d_2 + d_3 + d_4 + d_5 + d_6}{6}$$

where

$$d_1 = x_1 - x_0 = 3.2 - 0.7 = 2.5 \text{ cm}$$ $$d_2 = x_2 - x_1 = 6.5 - 3.2 = 3.3 \text{ cm}$$ $$d_3 = x_3 - x_2 = 8.3 - 6.5 = 1.8 \text{ cm}$$ $$d_4 = x_4 - x_3 = 10.0 - 8.3 = 1.7 \text{ cm}$$ $$d_5 = x_5 - x_4 = 11.5 - 10.0 = 1.5 \text{ cm}$$ $$d_6 = x_6 - x_5 = 15.5 - 11.5 = 4.0 \text{ cm}$$ $$d_{avg} = \frac{2.5 + 3.3 + 1.8 + 1.7 + 1.5 + 4.0}{6} = 2.47 \text{ cm} \approx 2.5 \text{ cm} = 2.5 \times 10^{-2} \text{ m}.$$

Answer: $1.48 \times 10^{-1} \text{ m}; 2.5 \times 10^{-2} \text{ m}$.

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