Stuck in the middle of a frozen pond with only your physics book, you decide to put physics in action and throw the 6-kg book. If your mass is 54 kg and you throw the book at 14 m/s, how fast do you then slide across the ice? (Assume the absence of friction. Let the direction the ball is initially moving be the positive direction.)

Are you throwing a ball or a book?

Apply conservation of momentum.

To find out how fast you slide across the ice after throwing the book, we need to apply the principle of conservation of momentum. According to this principle, the momentum of an isolated system remains constant if no external forces act on it.

Before throwing the book, the momentum of the system is zero since both you and the book are at rest. After throwing the book, the momentum of the system should still be zero since there are no external forces acting on it.

The momentum of an object is given by the product of its mass and velocity. So, the momentum before throwing the book (when you are at rest) is:

Momentum_before = Mass_of_person x Velocity_of_person = (54 kg) x (0 m/s) = 0 kg·m/s

The momentum of the book before throwing is:

Momentum_of_book_before = Mass_of_book x Velocity_of_book = (6 kg) x (0 m/s) = 0 kg·m/s

The total momentum of the system before throwing is therefore:

Total_momentum_before = Momentum_before + Momentum_of_book_before = 0 kg·m/s + 0 kg·m/s = 0 kg·m/s

After throwing the book, let's assume you slide across the ice with a velocity of V_slide. The book will then move in the opposite direction with a velocity of -14 m/s.

The momentum of you sliding across the ice after throwing the book is:

Momentum_of_person_after = Mass_of_person x Velocity_of_person_after = (54 kg) x (V_slide)

The momentum of the book after throwing is:

Momentum_of_book_after = Mass_of_book x Velocity_of_book_after = (6 kg) x (-14 m/s) = -84 kg·m/s

The total momentum of the system after throwing should still be zero:

Total_momentum_after = Momentum_of_person_after + Momentum_of_book_after = 0 kg·m/s

Substituting the values, we can now solve for the velocity at which you slide across the ice:

(54 kg) x (V_slide) + (-84 kg·m/s) = 0 kg·m/s

54 kg·V_slide - 84 kg·m/s = 0 kg·m/s

54 kg·V_slide = 84 kg·m/s

V_slide = 84 kg·m/s / 54 kg

V_slide ≈ 1.56 m/s

Therefore, you would slide across the ice with a velocity of approximately 1.56 m/s.