In an elastic collision, both momentum and kinetic energy are conserved.

The initial momentum of the system is the sum of the momenta of both gliders before the collision. The final momentum of the system is the sum of the momenta of both gliders after the collision.

The initial kinetic energy of the system is the sum of the kinetic energies of both gliders before the collision. The final kinetic energy of the system is the sum of the kinetic energies of both gliders after the collision.

Let's denote:

m1 = 0.143 kg (mass of the first glider)
v1i = 0.740 m/s (initial velocity of the first glider)
m2 = 0.298 kg (mass of the second glider)
v2i = -2.17 m/s (initial velocity of the second glider, negative because it's moving to the left)
v1f = ? (final velocity of the first glider, what we're trying to find)
v2f = ? (final velocity of the second glider)

From the conservation of momentum, we have:

m1*v1i + m2*v2i = m1*v1f + m2*v2f (equation 1)

From the conservation of kinetic energy, we have:

0.5*m1*v1i^2 + 0.5*m2*v2i^2 = 0.5*m1*v1f^2 + 0.5*m2*v2f^2 (equation 2)

We have two equations and two unknowns (v1f and v2f). We can solve these equations simultaneously to find the values of v1f and v2f.

However, since we're only asked to find the magnitude of the final velocity of the 0.143 kg glider (v1f), we can rearrange equation 1 to find an expression for v2f in terms of v1f, and then substitute this into equation 2. This will give us an equation with only v1f as the unknown, which we can then solve to find the value of v1f.

Let's do this:

From equation 1, we have:

v2f = (m1*v1i + m2*v2i - m1*v1f) / m2

Substitute this into equation 2, we get:

0.5*m1*v1i^2 + 0.5*m2*v2i^2 = 0.5*m1*v1f^2 + 0.5*m2*((m1*v1i + m2*v2i - m1*v1f) / m2)^2

Solve this equation for v1f.

Question

In an elastic collision, both momentum and kinetic energy are conserved.

The initial momentum of the system is the sum of the momenta of both gliders before the collision. The final momentum of the system is the sum of the momenta of both gliders after the collision.

The initial kinetic energy of the system is the sum of the kinetic energies of both gliders before the collision. The final kinetic energy of the system is the sum of the kinetic energies of both gliders after the collision.

Let's denote:

m1 = 0.143 kg (mass of the first glider)
v1i = 0.740 m/s (initial velocity of the first glider)
m2 = 0.298 kg (mass of the second glider)
v2i = -2.17 m/s (initial velocity of the second glider, negative because it's moving to the left)
v1f = ? (final velocity of the first glider, what we're trying to find)
v2f = ? (final velocity of the second glider)

From the conservation of momentum, we have:

m1*v1i + m2*v2i = m1*v1f + m2*v2f   (equation 1)

From the conservation of kinetic energy, we have:

0.5*m1*v1i^2 + 0.5*m2*v2i^2 = 0.5*m1*v1f^2 + 0.5*m2*v2f^2   (equation 2)

We have two equations and two unknowns (v1f and v2f). We can solve these equations simultaneously to find the values of v1f and v2f.

However, since we're only asked to find the magnitude of the final velocity of the 0.143 kg glider (v1f), we can rearrange equation 1 to find an expression for v2f in terms of v1f, and then substitute this into equation 2. This will give us an equation with only v1f as the unknown, which we can then solve to find the value of v1f.

Let's do this:

From equation 1, we have:

v2f = (m1*v1i + m2*v2i - m1*v1f) / m2

Substitute this into equation 2, we get:

0.5*m1*v1i^2 + 0.5*m2*v2i^2 = 0.5*m1*v1f^2 + 0.5*m2*((m1*v1i + m2*v2i - m1*v1f) / m2)^2

Solve this equation for v1f.

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