A block at rest explodes into three equal parts. Two parts start moving along X and Y axes respectively with equal speeds of 10 m/s. Find the initial velocity of the third part.

Question

Philoid · Accepted Answer

Initial momentum P_i = 0 kg m/s

Let the mass of each part be m kg and velocity of the third part be v_xî + v_yĵ

Final momentum P_f = 10m î + 10m ĵ + m(v_x î +v_y ĵ)

Applying conservation of momentum, p_i = p_f

0 = 10m î + 10m ĵ + m(v_x î +v_y ĵ)

v_x î +v_y ĵ = -10 î -10 ĵ

⇒ v_x = -10 and v_y = -10

Magnitude of velocity of third part

Angle with the horizontal =

= 135° from positive x axis or 45° below the x axis.