Answer:
(a) The x-component of the second sphere's velocity is 0.775 m/s
(b) The y-component of the second sphere's velocity is -0.338 m/s
Step-by-step explanation:
Conservation of Linear Momentum
The principle of the conservation of linear momentum states that the total momentum of a closed system of particles is conserved while no external forces act on any part of it, regardless of the interaction between the particles. The momentum is a vector, thus we must analyze both axes in the calculations.
The momentum can be computed as

where m is the mass of the particle, and
is its velocity. In a system of two particles, the total initial momentum is

And the final momentum is

Since the total momentum is conserved

According to the conditions of the problem, both masses are identical and sphere 2 is initially at rest (v2=0), thus

Simplifying by m
![\vec v_1'+\vec v_2'=\vec v_1\text{ ......[1]}](https://img.qammunity.org/2021/formulas/physics/college/n4eyxeagjyxvx732irnh05wo7w655a784f.png)
We know that the first sphere has a velocity of 1.5 m/s to the right. This means that the vertical component of v1 is 0:

We also know after the collision this same sphere travels at 0.8 m/s at an angle of 25°. The components of this velocity are

(a) Solving the equation [1] for v2




The x-component of the second sphere's velocity is 0.775 m/s
(b) The y-component of the second sphere's velocity is -0.338 m/s