A 5.92 g object moving to the right at 17.1 cm/s makes an elastic head-on collision with an 11.84 g object that is initially at rest Find the velocity of the first object immediately after the collision. The acceleration of gravity is 9.8 m/s 2 .

v₁f = -5.7 cm/s

Explanation:

Assuming no external forces acting during the collision, total momentum must be conserved, as follows:

       

Rearranging terms, we have:

       

We also know that the collision is elastic, so total kinetic energy must be conserved , as follows:

       

Rearranging , and simplifying common terms, we have:

       

Replacing by the givens, doing some algebra and dividing (4) by (2), we find the following relationship:

       

Replacing the expression above in (1), as m₂ = 2*m₁, we can find the value of v₁f, as follows: