---
title: "A ball of mass \\(m\\) is moving horizontally with speed \\(v\\) toward a vertical racket face. The ball strikes the racket and remains in contact for a time interval \\(\\Delta t\\), after which it moves horizontally in the opposite direction with the same speed \\(v\\). In a second trial, an identical ball with the same initial speed is struck such that it also reverses direction with speed \\(v\\), but the contact time is reduced to \\(\\dfrac{\\Delta t}{2}\\). What is the magnitude of the average force \\(F_2\\) exerted by the racket on the ball in this second trial?"
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url: "https://nerd-notes.com/ubq/109470/"
date_modified: "2026-04-10T09:42:01+00:00"
---

# A ball of mass \(m\) is moving horizontally with speed \(v\) toward a vertical racket face. The ball strikes the racket and remains in contact for a time interval \(\Delta t\), after which it moves horizontally in the opposite direction with the same speed \(v\). In a second trial, an identical ball with the same initial speed is struck such that it also reverses direction with speed \(v\), but the contact time is reduced to \(\dfrac{\Delta t}{2}\). What is the magnitude of the average force \(F_2\) exerted by the racket on the ball in this second trial?

A ball of mass \(m\) is moving horizontally with speed \(v\) toward a vertical racket face. The ball strikes the racket and remains in contact for a time interval \(\Delta t\), after which it moves horizontally in the opposite direction with the same speed \(v\). In a second trial, an identical ball with the same initial speed is struck such that it also reverses direction with speed \(v\), but the contact time is reduced to \(\dfrac{\Delta t}{2}\). What is the magnitude of the average force \(F_2\) exerted by the racket on the ball in this second trial?

![A two-part diagram labeled 'Trial 1'. On the left, a ball of mass m moves right with a velocity vector v toward a vertical racket. On the right, the ball moves left with a velocity vector v away from the racket. The label 'time = Delta t' is placed between the two parts. A 'Trial 2' diagram below it is identical but labeled 'time = Delta t / 2'.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/ubq-frq-generatedstem-fig-1-1775814121-TZ2f6T.jpg)

- **A.** \(\dfrac{mv}{2 \Delta t}\)
- **B.** \(\dfrac{mv}{\Delta t}\)
- **C.** \(\dfrac{2mv}{\Delta t}\)
- **D.** \(\dfrac{4mv}{\Delta t}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109470/*