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Chapter 18: Problem 2

A car approaches you at \(50 \mathrm{km} / \mathrm{h}\). A fly inside the car is flying toward the back of the car at \(7 \mathrm{km} / \mathrm{h}\). From your point of view by the side of the road, the fly is moving at _______ \(\mathrm{km} / \mathrm{h}.\) a. 7 b. 28.5 c. 43 d. 57

Short Answer

Expert verified
43 km/h

Step by step solution

01

Understand the Problem

Identify the speeds given in the problem: The speed of the car is 50 km/h and the speed of the fly relative to the car is 7 km/h flying towards the back.
02

Determine the Direction of Motion

Since the fly is flying towards the back of the car, subtract its speed from the car's speed to find the fly's speed relative to a stationary observer.
03

Calculate the Speed Relative to the Observer

The car is moving forward at 50 km/h and the fly is moving backward at 7 km/h relative to the car. Therefore, the fly's speed relative to a stationary observer is: 50 km/h - 7 km/h = 43 km/h.
04

Choose the Correct Answer

From the calculated speed, the correct answer is option c. 43 km/h.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Speed Calculation
Speed calculation is the process of determining how fast an object is moving. In our exercise, we are given two speeds: one of the car and one of the fly inside it. The car is moving at 50 km/h and the fly is moving towards the back of the car at 7 km/h. To find the speed of the fly as seen by an observer standing still outside the car, we need to perform some basic arithmetic operations. This involves subtracting the speed of the fly from the speed of the car since they are moving in opposite directions. We get:
50 km/h - 7 km/h = 43 km/h.
This calculation shows how the fly's speed relative to the stationary observer is determined.
Reference Frames
Understanding reference frames is crucial in solving problems involving relative motion. A reference frame is a point of view from which we measure the position and speed of objects. In our exercise, there are two main reference frames: the stationary observer by the side of the road, and the moving car.
  • From the fly's point of view, it is moving at 7 km/h towards the back of the car.
  • From the car's perspective, it sees the fly speeding backward inside it.
  • From the observer's perspective, they observe the car moving at a steady rate of 50 km/h, and they need to calculate the fly's speed from this viewpoint.
Understanding reference frames helps us correctly apply the concept of relative motion to the problem.
Relative Velocity
Relative velocity is the velocity of an object as observed from a particular reference frame. It is a vector quantity that has both magnitude and direction. In the current scenario, the relative velocity of the fly concerning the car is 7 km/h backward. However, to find the fly's relative velocity as seen by the stationary observer, we need to combine this with the car's velocity of 50 km/h.
Since the car moves forward while the fly moves backward inside it, we need to subtract the fly's speed from the car's speed:
Relative Velocity = Car's Speed - Fly's Speed = 50 km/h - 7 km/h = 43 km/h.
Thus, the fly's relative velocity as perceived by the observer is 43 km/h.
Conceptual Physics
Conceptual physics involves understanding the principles and concepts that govern physical phenomena. In the context of relative motion and speed calculations, comprehending these key ideas will help solve similar problems efficiently.
  • Observation Points: Different observers can see different speeds based on their frames of reference. For instance, the fly appears to move at 7 km/h to the car but at 43 km/h to an observer standing beside the road.
  • Vector Addition/Subtraction: When objects are moving in opposite directions, their speeds are subtracted to determine relative speed.
By grasping these foundational principles, students can approach problems by identifying the reference frame and applying the suitable vector operations to find the solution.

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Most popular questions from this chapter

Imagine a future astronaut traveling in a spaceship at 0.866 times the speed of light. Special relativity says that the length of the spaceship along the direction of flight is only half of what it was when it was at rest on Earth. The astronaut checks this prediction with a meter stick that he brought with him. Will his measurement confirm the contracted length of his spaceship? Explain your answer.

If a spaceship approaches you at \(0.5 c\), and a light on the spaceship is turned on pointing in your direction, how fast will the light be traveling when it reaches you? a. \(1.5 c\) b. between \(1.0 \mathrm{c}\) and \(1.5 \mathrm{c}\) c. exactly \(c\) d. between \(0.5 c\) and \(1.0 c\)

Go to the LIGO website (http://ligo.org/science.php) and read about gravitational waves. Click on "Sources of Gravitational Waves" and listen to the example. What are the differences among the four listed sources of gravitational waves? Click on "Advanced LIGO." What's new with the project?

If a spaceship approaching Earth at 0.9 times the speed of light shines a laser beam at Earth, how fast will the photons in the beam be moving when they arrive at Earth?

Imagine two protons traveling past each other at a distance \(d,\) with relative speed 0.9c. Compared with two stationary protons a distance \(d\) apart, the gravitational force between these two protons will be a. smaller, because they interact for less time. b. smaller, because the moving proton acts as if it has less mass. c. the same, because the particles have the same mass. d. larger, because the moving proton acts as if it has more mass.
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