The three-toed sloth is the slowest moving land mammal. On the ground, the sloth moves at an...

Question:

The three-toed sloth is the slowest moving land mammal. On the ground, the sloth moves at an average speed of 0.0330 m/s, considerably slower than the giant tortoise, which walks at 0.0800 m/s. After 10.2 minutes of walking, how much further would the tortoise have gone relative to the sloth?

Distance Between Two Moving Bodies


The distance between two moving bodies changes as time progresses. Since distance is path-dependent the path taken by the two is important. If they have different speed the gap between them increases as time progresses.

Answer and Explanation:


Given:

  • {eq}s_s = 0.0330\ \rm \frac{m}{s}{/eq} Speed of the sloth
  • {eq}s_t = 0.0800\ \rm \frac{m}{s}{/eq} Speed of the tortoise
  • {eq}t = 10.2\ \rm min = 612\ \rm s{/eq}

First, we solve for the distance covered by the sloth.

$$\begin{align} d_s &= s_st\\ d_s &= \left(0.0330\ \rm \frac{m}{s}\right)(612\ \rm s)\\ d_s &= 20.196\ \rm m \end{align} $$

Now we solve for the distance covered by the tortoise.

$$\begin{align} d_s &= s_st\\ d_s &= \left(0.0800\ \rm \frac{m}{s}\right)(612\ \rm s)\\ d_s &= 48.960\ \rm m \end{align} $$

Solving for the distance of the tortoise from the slot after 612 seconds.

$$\begin{align} d &= d_t - d_s\\ d &= 48.960\ \rm m - 20.196\ \rm m\\ d &= 28.764\ \rm m \end{align} $$

Therefore the distance of the tortoise from the sloth after 612 seconds is 28.764 m.


Learn more about this topic:

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How to Find the Distance Between a Point & a Line

from FTCE Mathematics 6-12 (026): Practice & Study Guide

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