Question

Question #30dd4

Answer 1

`-8 kgms^-1` or may be `+8 kgms^-1` as well .

Explanation:

The formula for momentum is `P = mv`, 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 * 20`, and so momentum is `4 kg m s^-1`.
When the ball returns, the velocity `v` will become `-v`. So, the final momentum becomes `-4 kgms^-1`.
`P_"final" - P_"initial" = DeltaP`
`= -4 kgms^-1 - 4kgms^-1`
`=-8 kgms^-1`

So `DeltaP = -8 kgms^-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 .

Answer 2

`-8` `kgms^-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 `m/s`

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

`color(brown)(200g=`

Since, `1g=1/1000kg`

`rarr200g=(2cancel00)/(10cancel00)kg`

`color(purple)(rarr=0.2kg`

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

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

Since, `1(km)/h=5/18 m/s`

`rarr72(km)/h=cancel72^4xx5/cancel18^1m/s`

`color(green)(rarr=20m/s`

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

Now, calculate momentum

`rarr0.2*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,

`rarr-4-4`

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

Hope that that helps!!! ☺♦☻