Aaron (mass 60 kg) catches his running cat (mass 5 kg) moving horizontally at 1.5 m/s. What is the speed of Aaron and his cat after the catch?

To determine the speed of Aaron and his cat after the catch, we need to apply the conservation of momentum principle. According to this principle, the total momentum before the catch should be equal to the total momentum after the catch.

The momentum of an object is given by the product of its mass and velocity.

Before the catch:
The momentum of Aaron and his cat before the catch is the sum of their individual momenta.

Momentum of Aaron before the catch = Mass of Aaron × Velocity of Aaron
= 60 kg × 0 m/s (since Aaron is stationary)

Momentum of the cat before the catch = Mass of the cat × Velocity of the cat
= 5 kg × 1.5 m/s (given velocity)

Since Aaron is stationary before the catch, his momentum is zero.

So, the total momentum before the catch is the momentum of the cat:

Total momentum before the catch = Momentum of the cat before the catch
= 5 kg × 1.5 m/s
= 7.5 kg·m/s

After the catch, Aaron and his cat move together with a common velocity.

Let's assume the final velocity of Aaron and his cat after the catch is V.

The total momentum after the catch is the combined momentum of Aaron and his cat:

Total momentum after the catch = (Mass of Aaron + Mass of the cat) × Velocity after the catch
= (60 kg + 5 kg) × V
= 65 kg × V

According to the conservation of momentum principle, the total momentum before and after the catch should be the same.

Total momentum before the catch = Total momentum after the catch

7.5 kg·m/s = 65 kg × V

Now, we can solve for V:

V = 7.5 kg·m/s / 65 kg
V ≈ 0.115 m/s

Therefore, the speed of Aaron and his cat after the catch is approximately 0.115 m/s.