Given, m1 and m2 are two masses, Initial speed of m2,u2=0 and height of m2 from ground =h.
Let tension in rope be T and acceleration of block be a. ∴ From force equation of body of mass m2, m2g−T=m2a . . . (i) Force of equation of body of mass m1, T=m1a . . . (ii) From Eqs. (i) and (ii), we have ⇒‌m2g−m1a‌‌=m2a ⇒‌m2g‌‌=a(m1+m2) ⇒‌a=‌
m2g
m1+m2
By using third equation of motion, v2−u2=2ah where, v is final speed and u is initial speed. ∴‌v2−02‌=2ah ⇒‌v‌=√2ah =√2×‌