Answer:
2.53 m/s
Step-by-step explanation:
From the law of conservation of momentum,
For an Elastic collision,
Total kinetic energy before collision = Total kinetic energy after collision
Ek₁ = 1/2mv²+1/2m'v'²................. Equation 1
Where Ek₁ = total kinetic energy before collision, m = mass of the first cart, v = final velocity of the first cart, m' = mass of the second cart, v' = final velocity of the second cart.
Given: Ek₁ = 96 J, m = 10 kg, m' = 2 kg, v' = 8 m/s.
Substitute into equation 1 and solve for the value of v.
96 = 1/2(10)(v²)+1/2(2)(8²)
96 = 5v²+64
5v² = 96-64
5v² = 32
v² = 32/5
v² = 6.4
v = √6.4
v = 2.53 m/s
Hence the final speed of the 10 kg mass = 2.53 m/s