Physics Problem. Any help would be awesome.?

A 2 kg block at rest on a horizontal surface suddenly explodes into two fragments, one 4.5 times heavier than the other. The heavier fragment slides 14 m along the horizontal surface before stopping. How far (in meters) does the lighter fragment slide? Assume that both fragments have the same coefficient of kinetic friction with the surface.


since all the forces involved in the explosion are internal to the system (of the block), the momentum of the block is conserved in the explosion...this means that if the smaller piece took mv momentum in one direction, the larger block had the same momentum immediately after the explosion

since the larger block is 4.5 times more massive, its velocity had to be 4.5 times less

we can find distance traveled from:


vf=final speed =0

v0=initial speed

a=acceleration (this is a negtive number which is the same for both since the coefficient of friction is the same for both)

d=distance traveled (14m for the smaller one)

so we find that: d=v0^2/2a

or that d depends on the square of initial velocity; since the initial velocity is 4.5 times less, distance traveled is 20.25 times less, or a distance = 14m/20.25=0.69m