# Math Help - [SOLVED] A sailboat of mass

1. ## [SOLVED] A sailboat of mass

A sailboat of mass m is moving with a momentum p. which of the following represents its kinetic energy?
a) mp
b) p2/2m
c) mp/3
d) 1/2 mp2
c) mp/2

2. Originally Posted by paulina
A sailboat of mass m is moving with a momentum p. which of the following represents its kinetic energy?
a) mp
b) p2/2m
c) mp/3
d) 1/2 mp2
c) mp/2
Hello, paulina,

$p=m\cdot v\ \Longrightarrow\ v=\frac{p}{m}$

The kinetic energy is $E_{kin}=\frac{1}{2}\cdot m\cdot v^2$. Plug in v into E and you'll get:

$E_{kin}=\frac{1}{2}\cdot m\cdot \left(\frac{p}{m}\right)^2$ = $\frac{p^2}{2m}$

Greetings

EB

3. Originally Posted by paulina
A sailboat of mass m is moving with a momentum p. which of the following represents its kinetic energy?
a) mp
b) p2/2m
c) mp/3
d) 1/2 mp2
c) mp/2
Sloppy question $\bold{p}$ is a vector quantity, $KE$ is a scalar, but the wording seems to treat the two of them as if they are scalars

Also what is meant by $\bold{p}^2$ is not specified, presumably it means $|\bold{p}|^2$.

RonL

4. Originally Posted by CaptainBlack
Sloppy question $\bold{p}$ is a vector quantity, $KE$ is a scalar, but the wording seems to treat the two of them as if they are scalars

Also what is meant by $\bold{p}^2$ is not specified, presumably it means $|\bold{p}|^2$.

RonL
In Physics, $\bold{p}^2$ is defined to be the Euclidean dot product (unless otherwise stated), thus there is no ambiguity.

Note that the scalar vs. vector argument can be used to throw out answers a), c), and c) .

-Dan