Two masses of 3.4 kg and 2.5 kg are accelerated from an initial speed of 5 m/s and 12 m/s, respectively. The distances traversed by the masses in the 5^ th second are 104 m and 129 m, respectively. The ratio of their momenta after 10 s is x 8 . The value of x is ________.

Step-by-step solution

The distance traversed in the n^ th second is given by S_n = u + a 2 (2n - 1) . For the first mass ( m₁ = 3.4 kg, u₁ = 5 m/s): 104 = 5 + a₁ 2 (2 5 - 1) 99 = 9a₁ 2 a₁ = 22 m/s ^2 For the second mass ( m₂ = 2.5 kg, u₂ = 12 m/s): 129 = 12 + a₂ 2 (2 5 - 1) 117 = 9a₂ 2 a₂ = 26 m/s ^2 Velocities of the masses after 10 s: v₁ = u₁ + a₁ t = 5 + 22 10 = 225 m/s v₂ = u₂ + a₂ t = 12 + 26 10 = 272 m/s Momenta of the masses after 10 s: p₁ = m₁ v₁ = 3.4 225 = 765 kg m/s p₂ = m₂ v₂ = 2.5 272 = 680 kg m/s Ratio of their momenta: p₁