Chapter 1.5, Problem 45E

a.

To determine

The position of the top of the lake relative to the ice surface.

Answer to Problem 45E

  $\text{The position of the top of the lake relative to the ice surface is 3743 meters}\text{.}$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Depth of the lake = 1200 meters}\text{.}\\ \text{Distance drilled by the scientists from the ice surface = 3623 meters}\text{.}\\ \text{Distance left to the top of the lake = 120 meters}\text{.}\end{array}$

Concept Used:

The position of the top of the lake relative to the ice surface is equal to the sum of the distance drilled by the scientist from the ice surface and the distance left to the top of the lake.

Calculation:

As per the given problem

  $\begin{array}{l}\text{Depth of the lake = 1200 meters}\text{.}\\ \text{Distance drilled by the scientists from the ice surface = 3623 meters}\text{.}\\ \text{Distance left to the top of the lake = 120 meters}\text{.}\end{array}$

Therefore,

  $\text{The position of the top of the lake relative to the ice surface = 3623 + 120 = 3743 meters}\text{.}$

Conclusion:

  $\text{The position of the top of the lake relative to the ice surface is 3743 meters}\text{.}$

b.

To determine

The position of the bottom of the lake relative to the ice surface.

Answer to Problem 45E

  $\text{The position of the bottom of the lake relative to the ice surface is 4943 meters}\text{.}$

Explanation of Solution

Given:

  $\text{The position of the top of the lake relative to the ice surface is 3743 meters}\text{.}$

  $\text{Depth of the lake = 1200 meters}\text{.}$

Concept Used:

The position of the bottom of the lake relative to the ice surface is the sum of the distance from the ice surface to the top of the lake and the depth of the lake.

Calculation:

As per the given problem;

  $\text{The position of the top of the lake relative to the ice surface is 3743 meters}\text{.}$

  $\text{Depth of the lake = 1200 meters}\text{.}$

Therefore;

  $\text{The position of the bottom of the lake relative to the ice surface = 3743 + 1200 = 4943 meters}\text{.}$

Conclusion:

  $\text{The position of the bottom of the lake relative to the ice surface is 4943 meters}\text{.}$