# Question 1.6: Finding components of vectors Here we will use vector compon...

Finding components of vectors Here we will use vector components to track the positions of Raoul and Maria as they set out walking from their aunt’s house. For simplicity, we will assume that the aunt’s house is at the origin of our coordinate system. Raoul walks a certain distance straight east and then a certain distance straight north. He ends up at a position that is 500 m from the house in a direction that is 35°north of east. Maria, instead, walks first straight west and then straight south. Her final position is 700 m from the starting point in a direction that is 55° south of west. How far did Raoul walk on the east leg of his trip? How far on the north leg? Similarly, how far did Maria walk on the west leg and how far on the south leg? Express these quantities in terms of displacement vectors and their components, using a coordinate system with the +x axis pointing east and the +y axis pointing north.

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Question: 1.3

## Mass is energy Here we will use the concept of significant figures in one of the most famous equations in all of physics. Einstein’s theory of relativity predicts that mass and energy are equivalent. For instance, the energy E corresponding to the mass m of an electron is given by Einstein’s ...

SET UP We find the needed numbers inside the back ...
Question: 1.4

## Espionage Now let’s use estimation to assess the viability of a familiar spy-movie scenario. An international spy escapes across the border with a billion dollars worth of gold in his suitcase. Is this possible? Would that amount of gold fit in a suitcase? Would the suitcase be too heavy to carry? ...

SET UP AND SOLVE We can guess at both the mass of ...
Question: 1.8

## Vector addition helps win a Porsche As in Example 1.7, the vectors in this example are specified in terms of magnitude and direction. The first thing we need to do is to find their components. Consider four finalists in a treasure hunt who are brought to the center of a large, flat field. Each is ...

SET UP The situation is shown in Figure 1.21. We h...
Question: 1.7

## Adding two vectors Now we’ll use the component method to add two vectors. We will use this technique extensively (in Chapter 4) when we begin to consider how forces act upon an object. Vector A has a magnitude of 50 cm and a direction of 30°, and vector B has a magnitude of 35 cm and a direction of ...

SET UP We set up a rectangular (Cartesian) coordin...
Question: 1.5

## Displacement of a cross-country skier In this problem we will use graphical vector addition to determine your final location on a cross-country ski trip. Suppose that on a cross-country ski trip, you travel 1.00 km north and then 2.00 km east. (a) How far and in what direction are you from your ...

SET UP Figure 1.13 is a scale diagram. By careful ...
Question: 1.2