Chapter 3, Problem 34Q

To determine

The rank of cars according to the stopping distance.

Answer to Problem 34Q

The rank of all cars,

$\begin{array}{ccc}\left(\text{a}\right)& m=1000\text{kg}& v=10\text{m/s}\\ \left(\text{b}\right)& m=1000\text{kg}& v=20\text{m/s}\\ \left(\text{c}\right)& m=1000\text{kg}& v=30\text{m/s}\\ \left(\text{d}\right)& m=3000\text{kg}& v=10\text{m/s}\\ \left(\text{e}\right)& m=2000\text{kg}& v=10\text{m/s}\\ \left(\text{f}\right)& m=2000\text{kg}& v=20\text{m/s}\\ \left(\text{g}\right)& m=2000\text{kg}& v=30\text{m/s}\\ \left(\text{h}\right)& m=3000\text{kg}& v=20\text{m/s}\end{array}\begin{array}{c}p=1\times {10}^4\text{kg}\text{.m/s}\\ p=2\times {10}^4\text{kg}\text{.m/s}\\ p=3\times {10}^4\text{kg}\text{.m/s}\\ p=3\times {10}^4\text{kg}\text{.m/s}\\ p=2\times {10}^4\text{kg}\text{.m/s}\\ p=4\times {10}^4\text{kg}\text{.m/s}\\ p=6\times {10}^4\text{kg}\text{.m/s}\\ p=6\times {10}^4\text{kg}\text{.m/s}\end{array}\begin{array}{c}\text{Rank}\text{5}\\ \text{Rank}\text{4}\\ \text{Rank}\text{3}\\ \text{Rank}\text{3}\\ \text{Rank}\text{4}\\ \text{Rank}\text{2}\\ \text{Rank}\text{1}\\ \text{Rank}\text{1}\end{array}$.

Explanation of Solution

Given information:

The mass and velocity of different cars are given by,

$\begin{array}{ccc}\left(\text{a}\right)& m=1000\text{kg}& v=10\text{m/s}\\ \left(\text{b}\right)& m=1000\text{kg}& v=20\text{m/s}\\ \left(\text{c}\right)& m=1000\text{kg}& v=30\text{m/s}\\ \left(\text{d}\right)& m=3000\text{kg}& v=10\text{m/s}\\ \left(\text{e}\right)& m=2000\text{kg}& v=10\text{m/s}\\ \left(\text{f}\right)& m=2000\text{kg}& v=20\text{m/s}\\ \left(\text{g}\right)& m=2000\text{kg}& v=30\text{m/s}\\ \left(\text{h}\right)& m=3000\text{kg}& v=20\text{m/s}\end{array}$

Concept Used:

Momentum, $p=mv$.

Calculation:

The stopping distance is directly proportional to the momentum.

The momentum of each car is,

$\begin{array}{ccc}\left(\text{a}\right)& m=1000\text{kg}& v=10\text{m/s}\\ \left(\text{b}\right)& m=1000\text{kg}& v=20\text{m/s}\\ \left(\text{c}\right)& m=1000\text{kg}& v=30\text{m/s}\\ \left(\text{d}\right)& m=3000\text{kg}& v=10\text{m/s}\\ \left(\text{e}\right)& m=2000\text{kg}& v=10\text{m/s}\\ \left(\text{f}\right)& m=2000\text{kg}& v=20\text{m/s}\\ \left(\text{g}\right)& m=2000\text{kg}& v=30\text{m/s}\\ \left(\text{h}\right)& m=3000\text{kg}& v=20\text{m/s}\end{array}\begin{array}{c}p=1\times {10}^4\text{kg}\text{.m/s}\\ p=2\times {10}^4\text{kg}\text{.m/s}\\ p=3\times {10}^4\text{kg}\text{.m/s}\\ p=3\times {10}^4\text{kg}\text{.m/s}\\ p=2\times {10}^4\text{kg}\text{.m/s}\\ p=4\times {10}^4\text{kg}\text{.m/s}\\ p=6\times {10}^4\text{kg}\text{.m/s}\\ p=6\times {10}^4\text{kg}\text{.m/s}\end{array}$

So, the rank of all cars according to stopping distance,

$\begin{array}{ccc}\left(\text{a}\right)& m=1000\text{kg}& v=10\text{m/s}\\ \left(\text{b}\right)& m=1000\text{kg}& v=20\text{m/s}\\ \left(\text{c}\right)& m=1000\text{kg}& v=30\text{m/s}\\ \left(\text{d}\right)& m=3000\text{kg}& v=10\text{m/s}\\ \left(\text{e}\right)& m=2000\text{kg}& v=10\text{m/s}\\ \left(\text{f}\right)& m=2000\text{kg}& v=20\text{m/s}\\ \left(\text{g}\right)& m=2000\text{kg}& v=30\text{m/s}\\ \left(\text{h}\right)& m=3000\text{kg}& v=20\text{m/s}\end{array}\begin{array}{c}p=1\times {10}^4\text{kg}\text{.m/s}\\ p=2\times {10}^4\text{kg}\text{.m/s}\\ p=3\times {10}^4\text{kg}\text{.m/s}\\ p=3\times {10}^4\text{kg}\text{.m/s}\\ p=2\times {10}^4\text{kg}\text{.m/s}\\ p=4\times {10}^4\text{kg}\text{.m/s}\\ p=6\times {10}^4\text{kg}\text{.m/s}\\ p=6\times {10}^4\text{kg}\text{.m/s}\end{array}\begin{array}{c}\text{Rank}\text{5}\\ \text{Rank}\text{4}\\ \text{Rank}\text{3}\\ \text{Rank}\text{3}\\ \text{Rank}\text{4}\\ \text{Rank}\text{2}\\ \text{Rank}\text{1}\\ \text{Rank}\text{1}\end{array}$.

Conclusion:

The rank of all cars,

$\begin{array}{ccc}\left(\text{a}\right)& m=1000\text{kg}& v=10\text{m/s}\\ \left(\text{b}\right)& m=1000\text{kg}& v=20\text{m/s}\\ \left(\text{c}\right)& m=1000\text{kg}& v=30\text{m/s}\\ \left(\text{d}\right)& m=3000\text{kg}& v=10\text{m/s}\\ \left(\text{e}\right)& m=2000\text{kg}& v=10\text{m/s}\\ \left(\text{f}\right)& m=2000\text{kg}& v=20\text{m/s}\\ \left(\text{g}\right)& m=2000\text{kg}& v=30\text{m/s}\\ \left(\text{h}\right)& m=3000\text{kg}& v=20\text{m/s}\end{array}\begin{array}{c}p=1\times {10}^4\text{kg}\text{.m/s}\\ p=2\times {10}^4\text{kg}\text{.m/s}\\ p=3\times {10}^4\text{kg}\text{.m/s}\\ p=3\times {10}^4\text{kg}\text{.m/s}\\ p=2\times {10}^4\text{kg}\text{.m/s}\\ p=4\times {10}^4\text{kg}\text{.m/s}\\ p=6\times {10}^4\text{kg}\text{.m/s}\\ p=6\times {10}^4\text{kg}\text{.m/s}\end{array}\begin{array}{c}\text{Rank}\text{5}\\ \text{Rank}\text{4}\\ \text{Rank}\text{3}\\ \text{Rank}\text{3}\\ \text{Rank}\text{4}\\ \text{Rank}\text{2}\\ \text{Rank}\text{1}\\ \text{Rank}\text{1}\end{array}$.