A 5.4 kg soccer ball moving to the right at 5.6 m/s collides with a 7.6 kg basketball moving to the left at 3.8 m/s. The soccer ball bounces left at 6.5 m/s after the collision. What is the speed of the basketball after the collision?
5.4 (5.6) - 7.6(3.8) = 5.4(-6.5) + 7.6 v
Thanks!
To find the speed of the basketball after the collision, we can use the law of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision.
Let's break down the problem step by step:
Step 1: Calculate the initial momentum of the system.
The initial momentum is the sum of the individual momenta of the soccer ball and the basketball before the collision.
Momentum = mass × velocity
For the soccer ball:
Mass of soccer ball = 5.4 kg
Velocity of soccer ball = 5.6 m/s
Momentum of soccer ball = 5.4 kg × 5.6 m/s = 30.24 kg·m/s
For the basketball:
Mass of basketball = 7.6 kg
Velocity of basketball = -3.8 m/s (negative since it is moving to the left)
Momentum of basketball = 7.6 kg × (-3.8 m/s) = -28.88 kg·m/s (note the negative sign)
Total initial momentum = momentum of soccer ball + momentum of basketball
= 30.24 kg·m/s + (-28.88 kg·m/s)
= 1.36 kg·m/s
Step 2: Calculate the final momentum of the system.
The final momentum is the sum of the individual momenta of the soccer ball and the basketball after the collision.
For the soccer ball:
Velocity after the collision = -6.5 m/s (leftward)
Momentum of soccer ball after the collision = mass × velocity
= 5.4 kg × (-6.5 m/s)
= -35.1 kg·m/s (note the negative sign)
For the basketball:
Let's assume the velocity of the basketball after the collision is v.
Momentum of basketball after the collision = mass × velocity
= 7.6 kg × v
= 7.6v kg·m/s
Total final momentum = momentum of soccer ball after the collision + momentum of basketball after the collision
= -35.1 kg·m/s + 7.6v kg·m/s
Step 3: Apply the law of conservation of momentum.
According to the law of conservation of momentum, the total initial momentum should be equal to the total final momentum.
Total initial momentum = Total final momentum
1.36 kg·m/s = -35.1 kg·m/s + 7.6v kg·m/s
Rearranging the equation, we have:
7.6v kg·m/s = 1.36 kg·m/s + 35.1 kg·m/s
7.6v kg·m/s = 36.46 kg·m/s
Dividing both sides by 7.6 kg·m/s:
v = 36.46 kg·m/s / 7.6 kg·m/s
v ≈ 4.79 m/s
Therefore, the speed of the basketball after the collision is approximately 4.79 m/s.