Calculating Momentum for 1kg Ball Falling Freely

[JayK]

1. The problem statement, all variables and given/known
How long does a 1kg ball to reach the momentum of 75.5kgm/s if it free falls?

Homework Equations

Momentum= mass x velocity
F = (m x change in velocity) / change in time

The Attempt at a Solution

I used the first formula to find the velocity, which is 75.5m/s but I'm not sure what to do next.

 

[scottdave]

Do you know the formulas for motion with constant acceleration? V_final = V_initial + acceleration*time.

 

[PeterO]

1. The problem statement, all variables and given/known
How long does a 1kg ball to reach the momentum of 75.5kgm/s if it free falls?

Homework Equations

Momentum= mass x velocity
F = (m x change in velocity) / change in time

The Attempt at a Solution

I used the first formula to find the velocity, which is 75.5m/s but I'm not sure what to do next.

How long - there is a question of time.
does a 1 kg ball - there is mass
take to reach a momentum of 75.5 - there is momentum.
if you are dealing with momentum and time I would be considering Impulse.

 

[haruspex]

if you are dealing with momentum and time I would be considering Impulse.

Impulse is (change of) momentum, so that doesn't bring time in. What does connect momentum with time?

 

[PeterO]

Impulse is (change of) momentum, so that doesn't bring time in. What does connect momentum with time?

Not sure why you put "change of" in brackets? It is that very change that brings time in! Also to simply say "Impulse is momentum" is to utter a falsehood. Both quantities do share a common unit, but then so do Work and Energy, and we don't say they are the same thing.

 

[haruspex]

Not sure why you put "change of" in brackets?

So as to emphasise that impulse and momentum are dimensionally equivalent, which is what allows adding the one to the other.

to simply say "Impulse is momentum" is to utter a falsehood.

That's why I qualified it by noting that impulse is a delta to momentum, like displacement is a delta to position.

It is that very change that brings time in

It does not bring time in since the time taken for the change in momentum is immaterial to the impulse. To bring time in we would need to be considering rate of change (which is indeed helpful in this question).

 

[PeterO]

So as to emphasise that impulse and momentum are dimensionally equivalent, which is what allows adding the one to the other.

That's why I qualified it by noting that impulse is a delta to momentum, like displacement is a delta to position.

It does not bring time in since the time taken for the change in momentum is immaterial to the impulse. To bring time in we would need to be considering rate of change (which is indeed helpful in this question).

The object was in free-fall, so once we know what value of g we are to use for the problem, we know the Force acting, which with time will give the impulse and thus the change in momentum - and the answer to "How long ..."

 

[haruspex]

the Force acting,

Which is the answer to my question in post #4.