A can of Coke moving 15.6 m/s toward the right(the positive direction) collides with a can of Pepsi moving 3.21 m/s toward the left, and both cans are badly crunched. If the final velocity of the can of Coke is 2.48 m/s still toward the right, then what is the final velocity of the can of Pepsi? Assume the two cans have equal masses.
To find the final velocity of the can of Pepsi, 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, provided there are no external forces acting on the system.
Momentum is defined as the product of the mass and velocity of an object. Let's denote the initial velocity of the can of Coke as v1 (15.6 m/s), the initial velocity of the can of Pepsi as v2 (-3.21 m/s), the final velocity of the can of Coke as vf1 (2.48 m/s), and the final velocity of the can of Pepsi as vf2 (unknown).
Since the two cans have equal masses, we can say that m1 = m2, where m1 and m2 are the masses of the cans of Coke and Pepsi, respectively.
According to the conservation of momentum, the initial momentum is equal to the final momentum.
m1 * v1 + m2 * v2 = m1 * vf1 + m2 * vf2
Substituting the given values:
m1 * 15.6 + m2 * (-3.21) = m1 * 2.48 + m2 * vf2
Since the masses of the cans are equal (m1 = m2), we can simplify the equation:
15.6 - 3.21 = 2.48 + vf2
12.39 = 2.48 + vf2
Subtracting 2.48 from both sides:
12.39 - 2.48 = vf2
vf2 = 9.91 m/s
Therefore, the final velocity of the can of Pepsi is 9.91 m/s toward the left.