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Chapter 3: Problem 65

Two cars are driving toward each other on a straight, flat Kansas road. The Jeep Wrangler is traveling at \(82 \mathrm{km} / \mathrm{h}\) north and the Ford Taurus is traveling at \(48 \mathrm{km} / \mathrm{h}\) south, both measured relative to the road. What is the velocity of the Jeep relative to an observer in the Ford?

Short Answer

Expert verified
Answer: The relative velocity of the Jeep Wrangler with respect to an observer in the Ford Taurus is 130 km/h in the north direction.

Step by step solution

01

Convert Velocities to the Same Units

Since the velocities are given in km/h, there is no need to change the units.
02

Determine Whether Velocities Are Positive or Negative

Since they are in opposite directions (north and south), we should assign positive and negative signs based on their directions. Let's consider the north direction as positive and the south direction as negative: Jeep Wrangler velocity: \(+82 \mathrm{km/h}\) Ford Taurus velocity: \(-48 \mathrm{km/h}\)
03

Calculate Relative Velocity

To find the velocity of the Jeep Wrangler relative to the Ford Taurus, subtract the velocity of the Ford Taurus from the velocity of the Jeep Wrangler: Relative velocity (Vr) = Velocity of Jeep Wrangler - Velocity of Ford Taurus Vr = \(+82 \mathrm{km/h} - (-48 \mathrm{km/h})\)
04

Simplify the Equation

Simplify by adding the two velocities: Vr = \(82 \mathrm{km/h} + 48 \mathrm{km/h}\)
05

Find the Relative Velocity

Add the velocities to find the relative velocity: Vr = \(130 \mathrm{km/h}\) (north direction, because the result is positive) Thus, the velocity of the Jeep Wrangler relative to an observer in the Ford Taurus is \(130 \mathrm{km/h}\) in the north direction.

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