# Question 30dd4

Nov 3, 2017

$- 8 k g m {s}^{-} 1$ or may be $+ 8 k g m {s}^{-} 1$ as well .

#### Explanation:

The formula for momentum is $P = m v$, where $P$ is momentum, $m$ is mass in kilograms, and $v$ is velocity.
Now we have to convert 72km/h into m/s: 72000/3600 ×1000 = 20ms^-1
Now calculate initial momentum: $P = 0.2 \cdot 20$, and so momentum is $4 k g m {s}^{-} 1$.
When the ball returns, the velocity $v$ will become $- v$. So, the final momentum becomes $- 4 k g m {s}^{-} 1$.
${P}_{\text{final" - P_"initial}} = \Delta P$
$= - 4 k g m {s}^{-} 1 - 4 k g m {s}^{-} 1$
$= - 8 k g m {s}^{-} 1$

So $\Delta P = - 8 k g m {s}^{-} 1$
But if we consider that initial velocity is negative we get the answer that is additive inverse of what we got earlier , that's +8 .

Actually the momemtum hasn't changed just its direction reversed . So , there's an addition of a '-' ve sign .

Nov 5, 2017

$- 8$ $k g m {s}^{-} 1$

#### Explanation:

The formula for momentum is

color(blue)(sf( momentum=massxxvelocity

Where, the mass is expressed in kilograms and the velocity is expressed in $\frac{m}{s}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We need to convert our known values in the coventional units

color(brown)(200g=

Since, $1 g = \frac{1}{1000} k g$

$\rightarrow 200 g = \frac{2 \cancel{00}}{10 \cancel{00}} k g$

color(purple)(rarr=0.2kg

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

color(brown)(72(km)/h=

Since, $1 \frac{k m}{h} = \frac{5}{18} \frac{m}{s}$

$\rightarrow 72 \frac{k m}{h} = {\cancel{72}}^{4} \times \frac{5}{\cancel{18}} ^ 1 \frac{m}{s}$

color(green)(rarr=20m/s

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now, calculate momentum

$\rightarrow 0.2 \cdot 20$

rArrcolor(green)(4  color(green)(kgms^-1

We need to find the change in momentum

color(violet)(sf"change in momentum"="Final momentum"- "Initial momentum"

Since, the ball returns with the same momentum and in the opposite direction,

$\rightarrow - 4 - 4$

color(green)(rArr-8 color(green)(kgms^-1#

Hope that that helps!!! ☺♦☻
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