#"given :"#
#m_g: " mass of gun ,"m_g=1500" "kg#
#v_g :" velocity of gun before the shell is fired ,"v_g=0#
#m_s: " mass of shell , "m_s=10" "kg#
#v_s: "velocity of shell ,"v_s=400" "m/s#
#v_r: "the recoil velocity of the gun , "v_r=?#
#"You can solve using the principle of conservation of momentum."#
#"you should calculate the total momentum before the shell is fired."#
#"let "vec P_b " be the total momentum before the shell is fired."#
#"As the velocity of gun before the shell is fired equals zero,"#
#"its momentum is zero"#
#P_g=0#
#"As the velocity of the shell before the shell is fired equals zero,"#
#"its momentum is zero"#
#P_s=0#
#"Therefore ;"#
#P_b=P_g+P_s=0+0=0#
#"............................................................"#
#"let "vec P_a " be the total momentum after the shell is fired" #
#P_g=m_g*v_r" gun's momentum after the shell is fired"#
#P_g=1500*v_r#
#P_s=m_s*v_s" the shell's momentum after "#
#P_s=10*400=4000" "kg*m/s#
#vec P_a=vec P_g+vec P_s#
#vec P_a=1500*v_r+4000#
#"..............................................."#
#"As the momentum is conserved, we can write in the fallowing"#
#"equation "#
#P_b=P_a#
#0=1500*v_r+4000#
#1500*v_r=-4000#
#15cancel(00)*v_r=-40cancel(00)#
#v_r=-40/15#
#v_r=-2.67 " "m/s#
