An object at rest on a flat, horizontal surface explodes into two fragments, one seven times as massive as the other. The heavier fragment slides 5.60 mm before stopping. How far does the lighter fragment slide

M1 + M2 = 0   total momentum before explosion = momentum after explosion where M1 is the lighter fragment

M1 V1 + 7 M1 V2 = 0

V2 = -V1 / 7      

The lighter fragment will slide 7 times as far - 39.2 mm because it must have 7 times as much velocity - assuming the distance slid is proportional to the original velocity

it's a b and