Question

A bomb splits in to three identical parts. If two pieces are moving at right angles to each other with
same velocity v m/s, the velocity of third fragment is:
A) V
B) V/2
C) 2v
D) v√2
E) None​

Answer 1

Given Info : A bomb splits into three identical parts. if two pieces are moving at right angles to each other with the same velocity v m/s.

To find : the velocity of the 3rd fragment is...

solution : initial momentum of bomb is zero because there's no any motion.

after explosion, bombs splits into three identical fragment. two piece are moving at right angles to each other with speed v m/s.

let first moves along x direction while 2nd moves along y direction

let velocity of 3rd fragment is x m/s

now, final momentum = momentum of 1st fragment + momentum of 2nd + momentum of 3rd

= mv i + mv j + mx

as there is no external force acting on the system.

linear momentum must be conserved.

i.e., initial linear momentum = final linear momentum

⇒0 = mv i + mv j + mx

⇒mx = -mv (i + j)

⇒x = -v(i + j)

now magnitude of x = v√(1² + 1²) = v√2

Therefore the velocity of 3rd fragment is v√2 m/s