Projectile problem (This is a quickie)

[gcombina]

Hello, I need help on my basic math

This is the problem
A projectile is launches with 200kg.m/s of momentum and 1000 J of kinetic energy. What is the mass of the projectile.
(a) 20 kg

This is my math:

P = mv so
m = P/v
m = (200 kg.m/s)/v

KE = 1000 J
1000 J = 1/2 mv ^2
1000 J = 1/2 (mv) v
1000 J = 1/2 (200) v
v = 10 J

IF m = 200/v
m= (200 kg.m/s)/ (10 J)
m= (200 kg.m/s) / (10 NM)
m = (200 kg.m/s) / (10 ma.m)
m = (200 kg.m/s) / (10 kg.m/s.m)
m = (20/m) WHY IS THAT I HAVE THIS ANSWER?? 20/M? Instead of 20kg?

 

[NascentOxygen]

Both sides of every equation has units, including this one:
1000 J = 1/2 (200) v

You wrote v = 10 J
but v does not have units of Joules.

 

[Nathanael]

1000 J = 1/2 mv ^2
1000 J = 1/2 (mv) v
1000 J = 1/2 (200) v
v = 10 J

You forgot that the 200 has units of kg*m/s so when you divide Joules by kg*m/s you get m/s
So the answer is v=10 m/s

m= (200 kg.m/s)/ (10 J)
m= (200 kg.m/s) / (10 NM)
m = (200 kg.m/s) / (10 ma.m)
m = (200 kg.m/s) / (10 kg.m/s.m)
m = (20/m) WHY IS THAT I HAVE THIS ANSWER?? 20/M? Instead of 20kg?

Now try it with 10 m/s instead of 10 J and see if it works out.

 

[gcombina]

when I divide J/(kg*m/s), I get m/s? how so??

isn't J = NM?

so it would be [(nm) / (kg*m/s )] ?

 

[Nathanael]

when I divide J/(kg*m/s), I get m/s? how so??

isn't J = NM?

so it would be [(nm) / (kg*m/s )] ?

Yes, and a Newton is $kg*m/s^{2}$ so a Joule is $kg*m^{2}/s^{2}$
So divide $kg*m^{2}/s^{2}$ (Joules) by $kg*m/s$ and what do you get?

 

[NascentOxygen]

when I divide J/(kg*m/s), I get m/s? how so??

isn't J = NM?

so it would be [(nm) / (kg*m/s )] ?

This is where mastery and easy recall of equations is important.

W=Fs
But F=ma

So W=mas
This tels you that the Joule is a kg m m / sec²

 

[gcombina]

@nascent Oxygen

I am sorry , I do not understand ...what is fs? what is mas?

 

[gcombina]

@nathaneal,
thanks!

 

[NascentOxygen]

@nascent Oxygen

I am sorry , I do not understand ...what is fs? what is mas?

These are equations you must commit to memory. They are your tools of trade.

W=F.s where F is force & s is displacement (both F and s are vectors).

F=m.a where F is force & a is acceleration (both a anf F are vectors).