Answer:2.33 m/s
Explanation:
Given
4 kg mass is moving towards North at [tex]u_1=5\ m/s[/tex]
and 6 kg mass is moving towards the west at [tex]u_2=2\ m/s[/tex]
They collide inelastically i.e. stick together
Conserving momentum in the horizontal direction(west)
[tex]\Rightarrow 4\times 0+6\times 2=(4+6)v_x\quad \quad\ (v_1=\text{velocity of combined mass in west direction})\\\Rightarrow v_x=\dfrac{12}{10}=1.2\ m/s[/tex]
Conserving momentum in the vertical direction(North)[tex]\Rightarrow 4\times 5+6\times0=(4+6)v_y\quad \quad\ (v_y=\text{velocity of combined mass in North direction})\\\Rightarrow v_y=\dfrac{20}{10}=2\ m/s[/tex]
Net velocity is the vector sum of two velocities whose magnitude is given by
[tex]\left | v\right |=\sqrt{v_x^2+v_y^2}\\\left | v\right |=\sqrt{1.2^2+2^2}=2.33\ m/s[/tex]
The velocity of 4 kg mass will be the same as the combined mass because both the mass are moving together.
