A 0.50 kg ball is moving with a velocity of 8.0 m/s along a horizontal floor. It hits another ball with a mass of 0.80 kg and moving at 10.0 m/s in the opposite direction. If the first ball bounces back with a velocity of 12 m/s, with what velocity and in what direction will the second ball go after collision?

a car starts rest at 2m/s at a uniform speed of 5m/s(square) what is the time interval?

To solve this problem, we can apply the principle of conservation of momentum, which states that the total momentum before an interaction is equal to the total momentum after the interaction.

Momentum (p) is defined as the product of an object's mass (m) and its velocity (v):

p = m * v

In this case, we have two balls in a collision, so we need to calculate the total momentum before and after the collision for both balls.

Before the collision, the momentum of the first ball (m1) is given by:

p1_initial = m1 * v1_initial (where m1 = 0.50 kg and v1_initial = 8.0 m/s)

Similarly, the momentum of the second ball (m2) before the collision is:

p2_initial = m2 * v2_initial (where m2 = 0.80 kg and v2_initial = -10.0 m/s, since it is moving in the opposite direction)

The negative sign indicates that the second ball is moving in the opposite direction.

Now, we need to calculate the total momentum before the collision:

Total momentum before collision = p1_initial + p2_initial

Next, after the collision, the first ball bounces back with a velocity of 12 m/s in the opposite direction. So its momentum (p1_final) is:

p1_final = m1 * v1_final (where v1_final = -12.0 m/s)

The second ball's velocity (v2_final) and momentum (p2_final) after the collision are what we need to find.

Using the conservation of momentum principle, we can set up the equation:

Total momentum before collision = Total momentum after collision

(m1 * v1_initial) + (m2 * v2_initial) = (m1 * v1_final) + (m2 * v2_final)

Now we can plug in the given values and solve for v2_final:

(0.50 kg * 8.0 m/s) + (0.80 kg * -10.0 m/s) = (0.50 kg * -12.0 m/s) + (0.80 kg * v2_final)

Simplifying this equation will give us the velocity (v2_final) and the direction in which the second ball moves after the collision.