An object at rest is suddenly broken apart into fragments a and b by an explosion. the fragment a acquires three times the kinetic energy of the fragment b. part a what is the ratio of their masse

Momentum will be conserved in one dimension in the explosion.

Given that the fragment a acquires three times the kinetic energy of the fragment b.  

Pinitial = pfinal ⇒ 0 =mₐv⁰ₐ+mьv⁰ь= 0 ⇒ v⁰ь = -mₐv⁰ₐ/mь

KE= 3KEь

⇒1/2 mₐv⁰ₐ² = 3 (1/2mьv⁰ь²) 

⇒1/2 mₐv⁰ₐ²  = 3/2 mь(-mₐv⁰ₐ/mь)²

⇒1/2 mₐv⁰ₐ²  = 3/2 mь(mₐ²v⁰ₐ²/mь²)

⇒1/2 x 2/3 = mₐ/mь= 1/3

Thus the ratio of the masses of the fragments is 1:3.    

Answer: fn = wcos50 = 38.89(9.81)(cos50) = 245.23 n