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Chapter 35: Problem 41

You are driving down a straight highway at a speed of \(v=50.0 \mathrm{~m} / \mathrm{s}\) relative to the ground. An oncoming car travels with the same speed in the opposite direction. With what relative speed do you observe the oncoming car?

Short Answer

Expert verified
Answer: The relative speed between the two cars is 100.0 m/s.

Step by step solution

01

Given values

The given values are: - Speed of car 1 relative to the ground, \(v_1 = 50.0 \mathrm{~m/s}\) - Speed of car 2 relative to the ground, \(v_2 = 50.0 \mathrm{~m/s}\)
02

Calculate relative speed between the two cars

Since both cars are moving in opposite directions, we simply add their individual speeds relative to the ground to determine the combined relative speed between them. $$v_\text{relative} = v_1 + v_2$$ Plugging in the given values, we get: $$v_\text{relative} = 50.0 \mathrm{~m/s} + 50.0 \mathrm{~m/s}$$
03

Solve for relative speed

Adding the speeds together, we find the relative speed between the two cars: $$v_\text{relative} = 100.0 \mathrm{~m/s}$$ This means the oncoming car is observed to be traveling at a relative speed of \(100.0 \mathrm{~m/s}\) with respect to the other car.

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