A block of mass M slides on a horizontal frictionless surface with a speed v_i =

Question

A block of mass M slides on a horizontal frictionless surface with a speed v_i = 20 m/sec in the^+x direction. An internal explosion occurs which causes the block to break into three pieces having masses m_1 = (0.2) M, m_2 = (0.5)M, and m_3 = (0.3)M respectively. After the explosion, piece 1 has a velocity of 10 m/sec in the -x direction and piece 3 has a velocity of 20 m/sec in the +x direction. What is the velocity of piece 2 after the explosion? a. 24 m/sec in the -x direction b. 32 m/sec in the -x direction c. zero d. 32 m/sec in the +x direction e. 24 m/sec in the +x direction

Explanation / Answer

here,

From Conservation of Momentum,

M*vi = m1*v1 + m2*v2 + m3*v3
m*20 = -0.2*m*10 + 0.5*m*v + 0.3m*20

solvign for Velocity fo second block, v
v = (20 - (0.3*20 - 0.2*10)) / 0.5

v = 32 m/s towards +x direction

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