Answer:
This is a problem of conservation of momentum in two dimensions. According to the law of conservation of momentum, the total momentum of a closed system is constant, regardless of the directions of the objects before and after they collide. Therefore, we can write the following equations for the x and y components of momentum:
m₁v₁ix + m₂v₂ix = m₁v₁fx + m₂v₂fx
m₁v₁iy + m₂v₂iy = m₁v₁fy + m₂v₂fy
where m₁ and m₂ are the masses of the ball and the pin, v₁i and v₂i are their initial velocities, and v₁f and v₂f are their final velocities. We can use the given information to plug in the values and solve for the unknowns. For the x-component, we have:
(6.35 kg)(8.49 m/s) + (1.59 kg)(0 m/s) = (6.35 kg)(v₁fx) + (1.59 kg)(20.1 m/s)(cos(-77°))
Solving for v₁fx, we get:
v₁fx = 6.62 m/s
The x-component of the ball’s final velocity is 6.62 m/s.
Explanation: