# Cat and Mouse First Meeting Distance: Solving a Physics Problem

• stripes
In summary, a mouse resting in a grass field spots a cat 10.0m away and starts racing towards it at a constant speed of 5.0 m/s. After a reaction time of 0.5 seconds, the mouse starts accelerating away from the cat at 1.5 m/s^2. The question asks how far away from the cat's initial position is the mouse when they first meet. The attempt at a solution involves using the equation x = vt + (1/2)at^2 for both the cat and mouse, but the algebraic mistake of using a minus sign instead of a plus sign leads to an incorrect solution. The correct approach is to subtract the reaction time from t for the mouse.

## Homework Statement

A mouse is resting in a grass field. At t=0 s, the mouse spots a cat that is 10.0m away and is racing towards him a at a constant speed of 5.0 m/s. After taking 0.5 s to react, the mouse starts accelerating from rest at 1.5 m/s^2 away from the cat. How far away from the cat's initial position is it when the cat and mouse first meet?

## Homework Equations

x = vt + (1/2)at^2

## The Attempt at a Solution

Okay so we start off by saying for the cat:

x = vt, because acceleration is zero

then for the mouse:

x - 10 = (1/2)a(t + 0.5)^2 because the mouse has initial velocity of zero

then, we combine these two to get:

(v cat)t - 10 = (1/2)a(t + 0.5)^2

(v cat)t - 10 = (1/2)at^2 + (1/2)at + (1/8)a <<< after expanding

0 = .75t^2 - 4.25t + 10.1875

using a quadratic solver, t does not exist (that is, it is not a real number).

Where did I go wrong? When I had this marked (above), I actually accidentally used 0 = .75t^2 - 4.25t - 10.1875 (note the MINUS sign before the 10.1875 instead of a plus from above), and i got time = 7.5 seconds. I used this time to figure out the distance, and I got 37 meters, and i got 9/10 for my solution.

After looking back i realized there is no solution, because my algebra was wrong.

What happened?

Think it over: When the mouse starts to accelerate the cat is already closer than 10 m to it.
The reaction time of the mouse means that it starts to move later. If you add the reaction time, it means that the mouse has a displacement already at t=0 before it started to move.

Place the origin somewhere and decide when you start to measure time. I suggest to start time when the mouse is set to move.
Write the coordinate of the mouse and the coordinate of the cat: they must be equal.

ehild

Ahh very true...so I should instead subtract 0.5 from t for the mouse...i will try this and see what i get!

Thank you!

## 1. What is the "cat and mouse question"?

The "cat and mouse question" is a classic problem in game theory that involves two players, a cat and a mouse, moving around on a chessboard. The goal of the game is for the cat to catch the mouse, while the mouse tries to avoid being caught.

## 2. What is the origin of the "cat and mouse question"?

The "cat and mouse question" was first introduced by mathematician Claude Shannon in his 1949 paper "Programming a Computer for Playing Chess". He used the game to demonstrate the concept of "minimax" strategies in game theory.

## 3. What are the rules of the "cat and mouse question"?

The cat and mouse take turns moving one space at a time, with the cat moving first. The cat can move in any direction, while the mouse can only move horizontally or vertically. The game ends when the cat catches the mouse or when the mouse reaches the edge of the board and escapes.

## 4. What is the significance of the "cat and mouse question"?

The "cat and mouse question" is often used as a simple example in game theory to demonstrate strategic thinking and decision-making. It has been studied in various fields, including mathematics, computer science, and economics, to understand different strategies and outcomes.

## 5. Can the mouse ever win in the "cat and mouse question"?

It is possible for the mouse to win in the "cat and mouse question" if the cat makes a wrong move or if the mouse is able to trap the cat in a corner. However, in most cases, the cat has the advantage and will eventually catch the mouse.