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Chapter 3: Problem 41

You are driving down a straight road at a speed of \(90 \mathrm{km} / \mathrm{h}\) and you see another car approaching you at a speed of \(110 \mathrm{km} / \mathrm{h}\) along the road. a. Relative to your own frame of reference, how fast is the other car approaching you? b. Relative to the other driver's frame of reference, how fast are you approaching the other driver's car?

Short Answer

Expert verified
a) 200 km/h, b) 200 km/h

Step by step solution

01

- Understand the Problem

Two cars are moving towards each other on a straight road. Your car is moving at a speed of 90 km/h, and the other car is moving at 110 km/h.
02

- Define Relative Velocity

Relative velocity is the velocity of one object as observed from the frame of reference of another object. When two objects are moving towards each other, their relative velocities add up.
03

- Calculate Relative Velocity from Your Frame of Reference

From your frame of reference, the other car's speed will be the sum of your speed and the other car's speed. Relative velocity = Your speed + Other car's speed \( v_{relative} = 90 \, \text{km/h} + 110 \, \text{km/h} = 200 \, \text{km/h} \)
04

- Calculate Relative Velocity from the Other Driver's Frame of Reference

From the other driver's frame of reference, your speed will appear to be the same as the sum of your speeds: Relative velocity = Other car's speed + Your speed \( v_{relative} = 110 \, \text{km/h} + 90 \, \text{km/h} = 200 \, \text{km/h} \)

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Key Concepts

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

frame of reference
In physics, a frame of reference is essentially a viewpoint from which you measure and observe properties like position, velocity, and acceleration of objects. Imagine you're standing at a bus stop, and a car passes by. From your perspective, the car is in motion. However, if you're sitting inside the car, you'd feel stationary while the bus stop seems to whiz past you.
This idea helps us with the following:
  • Understanding relative speed and motion between different objects.
  • Realizing that different frames of reference can provide different measurements.
In our problem, we use two frames of reference:
  • One from your perspective inside your car.
  • Another from the perspective of the driver in the other car.
relative motion
Relative motion is the calculation of the movement of an object concerning another moving object. It involves understanding how far apart these objects are moving from or towards each other.
Think of it as determining how fast one object seems to be moving when viewed from another moving object. For example, if you are running at 5 km/h and your friend is running towards you at the same speed, from your viewpoint your friend seems to be approaching very rapidly.
In the problem:
  • Your car is moving at 90 km/h.
  • The other car is moving towards you at 110 km/h.
To combine these motions into one observation, we sum their speeds, giving a relative motion value of 200 km/h. This sum tells us how fast the two cars are closing the distance from each viewpoint.
velocity addition
Velocity addition is a technique used to combine velocities from different frames of reference. When objects move towards each other in a straight line, their velocities add up to show how quickly they are approaching.
This works because:
  • You're adding two velocities directly to find the combined effect.
  • The direction and magnitude of each velocity contribute to the resultant velocity.
Let's see this in our problem:
  • You're driving at 90 km/h.
  • The other car is driving towards you at 110 km/h.
By adding these velocities, we find:
  • Relative velocity = 90 km/h + 110 km/h = 200 km/h.
The same addition applies no matter which viewpoint you pick, yielding symmetrical results.
This approach helps us visualize and calculate how objects interact in motion.

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Most popular questions from this chapter

When Earth catches up to a slower-moving outer planet and passes it in its orbit, the planet a. exhibits retrograde motion. b. slows down because it feels Earth's gravitational pull. c. decreases in brightness as it passes through Earth's shadow. d. moves into a more elliptical orbit.

The time it takes for a planet to come back to the same position relative to the Sun is called its______ period. a. synodic b. sidereal c. heliocentric d. geocentric

Galileo came up with the concept of inertia. What do we mean by inertia?

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