Final answer:
To find the speed of the second block after an elastic collision, conservation of momentum is used. However, to solve for the unknown velocity, the mass of the second block is required, which is not provided in the question.
Step-by-step explanation:
A block with mass m = 4.4 kg slides across a frictionless surface and collides in a perfectly elastic collision with a second block at rest. After the collision, we need to determine the velocity V of the second block. For a perfectly elastic collision, both momentum and kinetic energy are conserved. The initial momentum of the system is given by the moving block alone (since the second block is at rest), which is mvi = 4.4 kg × 8.4 m/s. After collision, the 4.4 kg block moves with a speed of 2.5 m/s in the reverse direction, so its momentum is -4.4 kg × 2.5 m/s.
To find the velocity of the second block, we use the conservation of momentum:
Initial momentum = Final momentum
mvi = -m× final velocity of block m + M× final velocity of block M
Solving for the final velocity of block M:
Final velocity of block M = (Initial momentum + m × final velocity of block m) / M
Inserting the known values:
Final velocity of block M = (4.4 kg × 8.4 m/s + (-4.4 kg × 2.5 m/s)) / M
We do not have the value of the mass M, so we cannot solve for the final velocity numerically without it. The student would need to provide the mass M to find the exact value of V, the speed of the second block after the collision.