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

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- Jul 26th 2006, 11:12 AMpaulina[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 - Jul 26th 2006, 11:27 AMearbothQuote:

Originally Posted by**paulina**

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

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

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

So it's answer b)

Greetings

EB - Jul 26th 2006, 12:10 PMCaptainBlackQuote:

Originally Posted by**paulina**

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

RonL - Jul 26th 2006, 12:50 PMtopsquarkQuote:

Originally Posted by**CaptainBlack**

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

-Dan