Neona is on a tricycle A, combined mass 62 kg, and Alyssia is on tricycle B, combined mass 54 kg. They are initially at rest, but they push off of each other. What is Neona's speed immediately after the push if Alyssia's is 4.2 m/s?
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the interaction is equal to the total momentum after the interaction.
The momentum of an object is defined as the product of its mass and velocity. Therefore, the momentum of a tricycle can be calculated by multiplying its mass by its speed.
Let's denote the speed of Neona's tricycle after the push as v₁ and the speed of Alyssia's tricycle after the push as v₂. We can set up the conservation of momentum equation as follows:
(m₁ * v₁) + (m₂ * v₂) = (m₁ * u₁) + (m₂ * u₂)
where:
m₁ = mass of Neona's tricycle (62 kg)
v₁ = speed of Neona's tricycle after the push (unknown)
m₂ = mass of Alyssia's tricycle (54 kg)
v₂ = speed of Alyssia's tricycle after the push (4.2 m/s)
u₁ = initial speed of Neona's tricycle (0 m/s since it is initially at rest)
u₂ = initial speed of Alyssia's tricycle (0 m/s since it is initially at rest)
Plugging in the given values, the equation becomes:
(62 kg * v₁) + (54 kg * 4.2 m/s) = (62 kg * 0 m/s) + (54 kg * 0 m/s)
Simplifying further:
62 kg * v₁ + (54 kg * 4.2 m/s) = 0 kg⋅m/s + 0 kg⋅m/s
62 kg * v₁ + 226.8 kg⋅m/s = 0 kg⋅m/s
To find Neona's speed (v₁), we need to isolate v₁ on one side of the equation. Let's move the known term to the other side:
62 kg * v₁ = -226.8 kg⋅m/s
Now, divide both sides by 62 kg to solve for v₁:
v₁ = (-226.8 kg⋅m/s) / 62 kg
v₁ ≈ -3.66 m/s
Therefore, Neona's speed immediately after the push is approximately -3.66 m/s. The negative sign indicates that Neona has moved in the opposite direction to the initial velocity of Alyssia's tricycle.