Answer: -26.67 m/s.
Explanation:To find the final velocity of the first ball, we can use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, as long as no external forces are involved.
First, let's calculate the initial momentum of each ball:
The initial momentum of the first ball (0.60 kg) is given by:
Initial momentum = mass × velocity = 0.60 kg × 20 m/s = 12 kg·m/s
The initial momentum of the second ball (1 kg) is given by:
Initial momentum = mass × velocity = 1 kg × (-15 m/s) = -15 kg·m/s (negative sign because it's moving in the opposite direction)
Now, let's calculate the total initial momentum:
Total initial momentum = initial momentum of the first ball + initial momentum of the second ball
Total initial momentum = 12 kg·m/s + (-15 kg·m/s) = -3 kg·m/s
Since there are no external forces involved, the total momentum before the collision is equal to the total momentum after the collision.
Let's assume that the final velocity of the first ball is v1 and the final velocity of the second ball is v2.
Using the conservation of momentum principle, we can write:
Total final momentum = final momentum of the first ball + final momentum of the second ball
Since we are given the final velocity of the second ball (13 m/s), we can calculate its final momentum:
Final momentum of the second ball = mass × final velocity = 1 kg × 13 m/s = 13 kg·m/s
Now, let's substitute the values into the equation:
Total final momentum = (0.60 kg × v1) + 13 kg·m/s
Since the total final momentum should be equal to the total initial momentum, we can set up the equation:
-3 kg·m/s = (0.60 kg × v1) + 13 kg·m/s
Now, let's solve for v1:
-3 kg·m/s - 13 kg·m/s = 0.60 kg × v1
-16 kg·m/s = 0.60 kg × v1
Dividing both sides of the equation by 0.60 kg:
(-16 kg·m/s) / 0.60 kg = v1
v1 ≈ -26.67 m/s