A 26.2 g marble sliding to the right at 62.0 cm/s overtakes and collides elastically with a 13.1 g marble moving in the same direction at 15.5 cm/s. After the collision, the 13.1 g marble moves to the right at 77.5 cm/s. Find the velocity of the 26.2 g marble after the collision.

I think you can do this with just the momentum equation

26.2*62+13.1*15.5=13.1*77.5+26.2*V

solve for V

Thank You So Much .

To find the velocity of the 26.2 g marble after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object can be calculated by multiplying its mass by its velocity. Therefore, the momentum of the 26.2 g marble before the collision can be calculated as:

Momentum1 = mass1 * velocity1

where mass1 = 26.2 g = 0.0262 kg (converting grams to kilograms) and velocity1 = 62.0 cm/s = 0.62 m/s (converting centimeters to meters).

Momentum1 = 0.0262 kg * 0.62 m/s = 0.0162 kg*m/s

Similarly, the momentum of the 13.1 g marble before the collision can be calculated as:

Momentum2 = mass2 * velocity2

where mass2 = 13.1 g = 0.0131 kg and velocity2 = 15.5 cm/s = 0.155 m/s.

Momentum2 = 0.0131 kg * 0.155 m/s = 0.00203 kg*m/s

According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore:

Total momentum before collision = Total momentum after collision

Momentum1 + Momentum2 = Momentum3 + Momentum4

where Momentum3 is the momentum of the 26.2 g marble after the collision and Momentum4 is the momentum of the 13.1 g marble after the collision.

0.0162 kg*m/s + 0.00203 kg*m/s = Momentum3 + 0.0131 kg * 0.775 m/s (converting 77.5 cm/s to meters per second)

0.01823 kg*m/s = Momentum3 + 0.0101545 kg * m/s

Momentum3 = 0.01823 kg*m/s - 0.0101545 kg * m/s

Momentum3 = 0.0080755 kg*m/s

Now, we can calculate the velocity of the 26.2 g marble after the collision by dividing the momentum (0.0080755 kg*m/s) by the mass (0.0262 kg):

velocity after collision = momentum / mass

velocity after collision = 0.0080755 kg*m/s / 0.0262 kg

velocity after collision = 0.3085 m/s