Question

A body of mass 1kg initially at rest explodes and breaks into 3 fragments of masses in the ratio 1:1:3. The two pieces of equal masses fly off perpendicular to each other with a speed of 30m/s each. What is the velocity of the heavier fragment

Answer 1

Let two lighter objects be A and B and heavier object be C

calculate mass of obects, solve for x

x+x+3x=1kg

mass of A =1/5, B=1/5 and C=3/5

since the object is at rest we can apply conservation of linear momentum

Let A move on x axis so its v=30 i (i = i cap)

Let B move on y axis so its v=30 j (j = j cap)

velocity of C=?

m(a)u(a)+m(b)u(b)+m(c)u(c)=MV (M=mass of object i.e 1 kg since the object was initially at rest so V=0)

m(a)u(a)+m(b)u(b)+m(c)u(c)=M(0)

m(a)u(a)+m(b)u(b)+m(c)u(c)=0

putting the values

1/5×30i + 1/5×30j + 3/5×v = 0

after solving v= -10i -10j

numerical value of v = √(10² + 10² ) = 10√ 2 or 10×1.41 = 14.1