You and your friend, both of mass 70 kg, are playing catch with a frisbee on frictionless ice. Initially, you are both at rest. You throw a 0.175 kg frisbee at 10 m/s horizontally at your friend, who catches it. After they catch the frisbee, what is the relative velocity between you and your friend in m/s?

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To find the relative velocity between you and your friend after they catch the frisbee, we need to consider the principle of conservation of momentum.

The momentum of an object is defined as the product of its mass and velocity. In an isolated system, the total momentum before an event (in this case, throwing the frisbee) is equal to the total momentum after the event.

Initially, both you and your friend are at rest, so your initial momentum is zero. When you throw the frisbee horizontally, it acquires a momentum of its own.

We can use the equation for momentum:

p = m * v

where p represents momentum, m is the mass of an object, and v is its velocity.

The momentum of the frisbee can be calculated as:

p_frisbee = m_frisbee * v_frisbee

In this case, the mass of the frisbee (m_frisbee) is 0.175 kg, and its velocity (v_frisbee) is 10 m/s.
So, the momentum of the frisbee before the catch is:

p_frisbee = 0.175 kg * 10 m/s = 1.75 kg·m/s

According to the conservation of momentum, the total momentum after the catch should also be 1.75 kg·m/s. Since your friend catches the frisbee, their momentum after the catch will contribute to the total momentum. Since there is no friction or external forces on the ice, the momentum should be conserved, and there is no net external force acting on the system.

Therefore, the relative velocity between you and your friend after they catch the frisbee can be found by dividing the total momentum by the combined mass of both of you.

p_total = p_you + p_friend

The combined mass of both of you is 70 kg + 70 kg = 140 kg.

The relative velocity (v_relative) can be calculated as:

v_relative = p_total / (m_you + m_friend)

Substituting the values:

v_relative = (1.75 kg·m/s) / 140 kg

Calculating this:

v_relative ≈ 0.0125 m/s

So, the relative velocity between you and your friend after they catch the frisbee is approximately 0.0125 m/s.