Question

In a high-speed football game, a running back traveling at $55.0 \%$ of the speed of light relative to the field throws the ball to a receiver running in the same direction at $65.0 \%$ of the speed of light relative to the field. The speed of the ball relative to the running back is $80.0 \%$ of the speed of light. a) How fast does the receiver perceive the speed of the ball to be? b) If the running back shines a flashlight at the receiver, how fast will the photons appear to be traveling to the receiver?

Name: Problem 83, Chapter 35: University Physics with Modern Physics
Uploaded: 2021-05-19T05:14:58-08:00
Duration: 2 min 33 s
Channel: Narayan Hari

   In a high-speed football game, a running back traveling at $55.0 \%$ of the speed of light relative to the field throws the ball to a receiver running in the same direction at $65.0 \%$ of the speed of light relative to the field. The speed of the ball relative to the running back is $80.0 \%$ of the speed of light.
a) How fast does the receiver perceive the speed of the ball to be?
b) If the running back shines a flashlight at the receiver, how fast will the photons appear to be traveling to the receiver?

University Physics with Modern Physics

Wolfgang Bauer, Gary… 2nd Edition

Chapter 35, Problem 83

Instant Answer

Solved by Expert Narayan Hari

05/19/2021

Step 1

This can be given by the equation: \[ U_{BF} = \frac{U_{RB} + V_{RF}}{1 + \frac{U_{RB}V_{RF}}{c^2}} \] where $ U_{RB} $ is the velocity of the ball relative to the running back, $ V_{RF} $ is the velocity of the running back relative to the field, and $ c $ Show more…

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In a high-speed football game, a running back traveling at $55.0 \%$ of the speed of light relative to the field throws the ball to a receiver running in the same direction at $65.0 \%$ of the speed of light relative to the field. The speed of the ball relative to the running back is $80.0 \%$ of the speed of light. a) How fast does the receiver perceive the speed of the ball to be? b) If the running back shines a flashlight at the receiver, how fast will the photons appear to be traveling to the receiver?

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Key Concepts

Relativistic Velocity Addition

In special relativity, when combining velocities from different moving frames, the speeds are not simply added as in classical mechanics. Instead, the relativistic velocity addition formula is used, ensuring that the resulting speed never exceeds the speed of light. This formula accounts for the warping of space and time at high speeds and is essential when dealing with objects moving at a significant fraction of the speed of light.

Invariance of the Speed of Light

A foundational principle of special relativity is that the speed of light in a vacuum is constant in all inertial reference frames. This means that regardless of the relative motion of the source and the observer, light will always travel at the same speed. This invariance has profound implications for the way time and space are measured and underpins many of the counterintuitive predictions of high-speed dynamics.

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