Question

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. What relative speed do you observe for the oncoming car?

Short answer

Answer: The relative speed between car A and car B is 100.0 m/s.

Step-by-step solution

Understand the given information

We have two cars moving in opposite directions. Car A is moving to the right with a speed of \(v_A = 50.0 \mathrm{~m/s}\). Car B is moving to the left, with a speed of \(v_B = -50.0 \mathrm{~m/s}\) (having a negative sign since it moves in the opposite direction).

Determine the relative velocity

To find the relative velocity of car B as observed from car A, we'll subtract car A's velocity from car B's velocity: \(v_{BA} = v_B - v_A\).

Calculate the relative velocity

Applying the formula, we have \(v_{BA} = (-50.0\mathrm{~m/s}) - (50.0\mathrm{~m/s}) = -100.0\mathrm{~m/s}\). Since the relative speed is a scalar quantity, we can take the absolute value of this result: \(|-100.0\mathrm{~m/s}| = 100.0\mathrm{~m/s}\).

Interpret the result

The relative speed between car A and car B is \(100.0\mathrm{~m/s}\). This means that, as observed from car A, car B is approaching at a speed of \(100.0\mathrm{~m/s}\), and vice versa.