**1) The initial momentum of the trophy is zero**

**2) The initial momentum of the bowling ball is 160 kg m/s**

**3) The total momentum before the collision is 160 kg m/s**

**4) The total momentum of the system after the collision is 160 kg m/s**

**5) The final velocity of the trophy is 32 m/s**

**Explanation:**

1)

The momentum of an object is given by

where

m is the mass of the object

v is its velocity

In this problem, the data for the trophy before the collision are:

m = 2 kg is the mass

v = 0 is its initial velocity

Therefore, the initial momentum of the trophy is

2)

Using the same equation used in part 1), the initial momentum of the bowling ball is

where

m is the mass of the bowling ball

v is its initial velocity

The data of the problem are

m = 8 kg is the mass

v = 20 m/s is the velocity

Substituting,

3)

The total momentum of the system before the collision is given by the sum between the initial momentum of the trophy and the initial momentum of the bowling ball:

where

is the initial momentum of the trophy

is the initial momentum of the ball

Here we have

Therefore, the total momentum is

4)

According to the** law of conservation of momentum**, for an isolated system (=no external unbalanced forces acting on the system), the total momentum of the system is conserved before and after the collision:

where

is the total momentum before the collision

is the total momentum after the collision

If we consider the system in the problem to be isolated (i.e. no frictional forces acting on the ball or the trophy), we can therefore say that the total momentum after the collision must be equal to the total momentum before the collision: therefore,

5)

We can write the total momentum after the collision as

where:

is the mass of the trophy

is the final velocity of the trophy

is the mass of the bowling ball

is the final velocity of the ball

Since we also know the value of the final total momentum,

we can solve the equation to find the velocity of the trophy:

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