Question

An object of mass 10m, traveling in the x-direction at 5 m/s, explodes into 3 parts. a. If the part with mass 2m has a speed of 5 m/s in the x-direction, what are the velocities (vi and v2) of the other two masses? b. What is the velocity of the center of mass after the explosion? Wy- 50 Am 10m 10 m/s 2 5 m/s

Answer 1

Solution:- Let us consider that mau 10m is moving in no direction (towards posidive axis) and after collision 2m continues to travel through n-axis and masses 4m and 4m travels in both x and y n-y plane. So, before explosion momentum in 10m is. 10m x 10 = 100m Ns (+x-axis) Now, after collision momentum of three parts in x-dirution 4 m X vicos 50° + 2m x 5 + 4m X ug cos 50° =t&mucos so 4 10m) NS Visins o u = 4mvicos 50 + 4mv₂cos 50 + 10o Doo VicOS 50° In the y-axis, there is zero movement for am which both 4m have some. So, Visinso netapptying momentum system after collision y - dirations in the in 4m Xu, sin so + 4mX (-u, sin 58) 4m sin so (ui-U2) Uz - Uasinsů

Momentum in y-axis before collision = 0 conservation byore So, applying momentum collision, we have 4msinsolv,-U2) = 0 Pulting in ③ we have smuicosso + 10m conscruation in a Now, diration wing momentum , we have 100m = 8m vicos 50° + 10m 0) 100 = 8vicos so° +10 - go= quicosso Vi = 17.5 mls I = V2 - 17.5ml So, Ans

Date: __ Page: (6) Velouty of centre of mass after collision in y-axis Vy = 4m x visins + 8 m X (-uisin soo 4m + um of cuntre of may after collision Velocity x-axis in Un= 4m x uicosso + 4m x Uz Cosso +2mXS um + 2m +4m un= 10ml Velouty of centre of may - Vun² + Uy² =10m/s) Ang