October 2nd, 2019, 10:23 AM  #1 
Member Joined: Feb 2018 From: Iran Posts: 56 Thanks: 3  Collision
A body is thrown upward with a velocity of 30m/s after 5s it explodes in two pieces, one of pieces move downward with a velocity of 5m/s find the velocity of second piece in m/s ??

October 2nd, 2019, 10:56 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,588 Thanks: 1432 
apply conservation of linear momentum

October 2nd, 2019, 11:36 AM  #3 
Senior Member Joined: Jun 2019 From: USA Posts: 310 Thanks: 162 
I don't understand the situation. If there's an "up," that means there's gravity. Should we assume standard gravity? I assume we're neglecting drag, and that 5 m/s is the instantaneous speed of the downwardmoving piece immediately after the explosion, yes? Even with these questions answered, we're missing information. To apply conservation of momentum, we need to know the mass ratio of the two pieces. If 5 % of the mass is going downward, it's going to be a lot different than if it's 95 %. 
October 2nd, 2019, 12:45 PM  #4 
Newbie Joined: Oct 2019 From: SV USA Posts: 3 Thanks: 1  
October 2nd, 2019, 12:58 PM  #5 
Senior Member Joined: Dec 2015 From: somewhere Posts: 734 Thanks: 98 
Downward velocity , $\displaystyle v=v_0 +gt$. Upward velocity , $\displaystyle v=v_0 gt$. 
October 2nd, 2019, 01:09 PM  #6 
Senior Member Joined: Sep 2015 From: USA Posts: 2,588 Thanks: 1432  
October 2nd, 2019, 01:12 PM  #7  
Senior Member Joined: Jun 2019 From: USA Posts: 310 Thanks: 162  Quote:
Gravity (and probably some amount of drag) are the only forces on the object, except during the explosion. Most explosions are fast enough to be treated as instantaneous relative to a fivesecond time frame, so we can model it as an instantaneous impulse. There's still not enough information to solve the problem, however.  
October 2nd, 2019, 03:42 PM  #8 
Senior Member Joined: Sep 2015 From: USA Posts: 2,588 Thanks: 1432 
Sometimes with incomplete problems like this you have to go ahead and make assumptions and call them out in the answer. In this problem I'd assume that both pieces are the same size and say so. Further, they want the instantaneous velocity immediately after the explosion. So gravity and any other forces don't enter into it as they don't have any time to cause an effect. so assuming the original piece had a mass of 2m and broke into 2 pieces of 1m each 30 x 2m = 5m + vm 60=5+v v=65 m/s 
October 2nd, 2019, 05:28 PM  #9 
Senior Member Joined: Jun 2019 From: USA Posts: 310 Thanks: 162 
OK, I guess whether or not gravity comes into play is a matter of punctuation. 1) A body is thrown upward with a velocity of 30 m/s. After 5 s, it explodes in two pieces. 2) A body is thrown upward, with a velocity of 30 m/s after 5 s. It explodes in two pieces. 
October 2nd, 2019, 06:38 PM  #10  
Senior Member Joined: Sep 2015 From: USA Posts: 2,588 Thanks: 1432  Quote:
30  9.8 x 5 = 19 m/s 38 = 5 + v v = 33 m/s  

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