Here we have perfectly inelastic collision. Perfectly inelastic collision is type of collision during which two objects collide, stay connected and momentum is conserved. Formula used for conservation of momentum is:

In case of perfectly inelastic collision v'1 and v'2 are same.
We are given information:
m₁=0.5kg
m₂=0.8kg
v₁=3m/s
v₂=2m/s
v'₁=v'₂=x
0.5*3 + 0.8*2 = 0.5*x + 0.8*x
1.5 + 1.6 = 1.3x
3.1 = 1.3x
x = 2.4 m/s
Answer:
0.0312J
Explanation:
Let x be the distance the staple moves:

And spring constant is 

Hence, the potential energy is 0.0312J
When a perfume bottle is opened, some liquid changes to gas and the fragrance spreads around the room because gases do not have a definite volume.
Hope this helps!
Let V = the volume of the balloon
Force of gravity = V * ?hot * g downward
Buoyant force = V * ?cool * g upward
Net upward force F = V * ?cool * g - V * ?hot * g
F = V g (?cool - ?hot)
Mass of the balloon m = V ?hot
a = F/m = V g (?cool - ?hot)/(V ?hot)
a = g(?cool/?hot - 1)
a = 9.8(1.29/0.93 - 1)
a = 3.79 m/s^2
<span>Answer is 3.79 m/s^2</span>