Data:
m₁ = 1.5kg
m₂ = 3.2kg
α = -30° (negative because it is below the x-xis)

= initial speed of object 1 = 4.5m/s

= <span>initial speed of object 2 = 0m/s

= final</span><span> speed of object 1 = 2.1m/s

= ?
</span>β = ?
Since the motion after the collision is in 2 dimentions, it is better to write the speeds with their components along the x and the y-axis:

= initial speed of object 1 along x-axis = 4.5m/s

= <span>initial speed of object 1 along y-axis = 0m/s
</span>

<span> = initial speed of object 2 along x-axis = 0m/s

= </span><span>initial speed of object 2 along y-axis = 0m/s
</span>

= final speed of object 1 along x-axis = 2.1 cos(-30) = 1.82m/s

= final speed of object 1 along y-axis = 2.1 sin(-30) = -1.05m/s
In this kind of collision, we have the conservation of momentum, therefore we can write the system:

Considering the terms that are zero, it becomes:

Let's face first the y-component:

=

therefore:

=

=

= 5.04m/s
Now, let's face the x-component:

=

=

=

= 1.26m/s
Now that we have the two components, we can find:

=

=

=
6.35m/sLastly, the angle can be found with trigonometry:
β = tan⁻¹(

) = tan⁻¹(<span>

) =
14°</span>