Abody of mass 1.5kg, traveling along the positive x axis with speed 4.5m/s, collides with another body b of mass 3.2kg which, initially is at rest. a is deflected and moves with a speed of 2.1m/s in a direction which is 30 degrees below the x axis. b is set in motion at angle b above the x axis. calculate the velocity of b after collision.,

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
= initial speed of object 2 = 0m/s
= final speed of object 1 = 2.1m/s
= ?
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
= initial speed of object 1 along y-axis = 0m/s
= initial speed of object 2 along x-axis = 0m/s
= initial speed of object 2 along y-axis = 0m/s

= 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/s

Lastly, the angle can be found with trigonometry:

β = tan⁻¹() = tan⁻¹() = 14°

The purpose of a lab is to do your "expirements" the importance of the topic is so you can now what the story is about and the last one is because no one is me with my question ( what is 3 over 4 x - 9 = 27 maybe you can )