An 84.9 kg man is standing on a frictionless ice surface when he throws a 2.00kg book at 11.1m/s. Do the man move in the same direction as the book or opposite of the book.

To determine whether the man will move in the same direction as the book or in the opposite direction, we can apply the law of conservation of momentum.

The law of conservation of momentum states that the total momentum before any event is equal to the total momentum after the event, as long as no external forces are acting on the system.

The momentum of an object can be calculated by multiplying its mass by its velocity. In this case, the momentum of the man before throwing the book is given by:

Momentum of the man = mass of the man × velocity of the man

Momentum of the man = 84.9 kg × 0 m/s (since the man is initially at rest)

The momentum of the book is given by:

Momentum of the book = mass of the book × velocity of the book

Momentum of the book = 2.00 kg × 11.1 m/s

Now, let's calculate the total momentum before the throwing event:

Total momentum before = Momentum of the man + Momentum of the book

Total momentum before = 0 + (2.00 kg × 11.1 m/s)

Total momentum before = 0 + 22.2 kg·m/s

Total momentum before = 22.2 kg·m/s

Since there are no external forces acting on the system, the total momentum before the event should be equal to the total momentum after the event. Therefore, the magnitude of the man's momentum after throwing the book should also be 22.2 kg·m/s.

Now, we need to determine the direction of the man's momentum. If the man moves in the same direction as the book, their momenta will have the same sign (+22.2 kg·m/s). If the man moves in the opposite direction, their momenta will have opposite signs (-22.2 kg·m/s).

Unfortunately, we do not have enough information to determine the exact direction of the man's momentum. The direction of the man's momentum will depend on how he throws the book and the resulting forces acting on him during the throwing action.