Answer:
The final speed of the 24 g marble after the collision is 0.21 m/s.
Explanation:
Given that,
Mass of the marble 1, m = 24 g = 0.024 kg
Initial speed of the marble 1, u = 23 cm/s = 0.23 m/s
Mass of the marble 2, m' = 10 g = 0.01 kg
Initial speed of the marble 2, u' = 20 cm/s = 0.2 m/s
After the collision,
Final speed of marble 2, v' = 22.5 cm/s = 0.225 m/s
We need to find the velocity of the 24.0 g marble after the collision. It is a case of elastic collision. Using the conservation of momentum as :
[tex]mu+m'u'=mv+m'v'[/tex]
v is the speed of 24.0 g marble after the collision.
[tex]mv=mu+m'u'-m'v'\\\\mv=0.024\times 0.23+0.01\times 0.2-0.01\times 0.225 \\\\v=\dfrac{0.00527}{0.024}\\\\v=0.21\ m/s[/tex]
So, the final speed of the 24 g marble after the collision is 0.21 m/s.
