Stuck in the middle of a frozen pond with only your physics book, you decide to put physics in action and throw the 9-kg book. If your mass is 45 kg and you throw the book at 10 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.)

What ball?

The momentum of the book is m1*v1 in +ve x-direction. Since there is no external force in the horizontal direction, the linear momentum of the 'book and you' system will be conserved. Therefore you would have the same magnitude of momentum in the opposite direction. If your momentum is m2*v2 =>

m1*v1 = m2*v2
v2 = (m1*v1)/m2
v2 = 9*10/45 = 2 m/s
So you slide at 2m/s in -ve x direction

I think my book has a typo. It should say book, not ball.

Probably you and not your book. #Proud

he

Well, being stuck on a frozen pond can definitely be a slippery situation! Let's slide into the answer using some physics humor.

Since there's no friction in this icy scenario, we can apply the conservation of momentum. The initial momentum is just the momentum of the book, which is the product of its mass (9 kg) and velocity (10 m/s). So, the initial momentum is 90 kg·m/s (sounds like a big deal).

Now, conservation of momentum tells us that the total momentum before and after an event is the same. Since you initially had no velocity (like a couch potato), your total momentum was zero.

When you throw the book, it gains momentum in the forward direction. So, to keep the total momentum zero after throwing the book, you will have to slide in the opposite direction. We can set up the equation like this:

9 kg * 10 m/s = (9 kg + 45 kg) * v

After solving, we find that the velocity you will slide at is approximately -2 m/s (don't worry, you won't disappear off the pond!). The negative sign simply indicates that you'll be sliding in the opposite direction of the book's initial motion.

So, get ready for a bit of a backwards ice dance! Just make sure to put on your clown shoes for some extra comedic effect.

To find out how fast you slide across the ice after throwing the book, we can apply the principle of conservation of momentum.

According to the conservation of momentum, the momentum before throwing the book should be equal to the momentum after throwing it.

The momentum of an object is given by the product of its mass and velocity. So, before throwing the book, the total momentum is the sum of your momentum and the book's momentum.

Before throwing the book:
Momentum of you = mass of you × velocity of you
Momentum of book = mass of book × velocity of book

Since the direction in which the book is thrown is considered the positive direction, the momentum of you initially is zero since you are at rest.

After throwing the book:
Momentum of you = mass of you × velocity of you (final)
Momentum of book = mass of book × velocity of book (final)

According to the conservation of momentum:
Momentum before = Momentum after

Therefore:
0 + (mass of book × velocity of book) = (mass of you × velocity of you (final)) + (mass of book × velocity of book (final))

Plugging in the given values:
0 + (9 kg × 10 m/s) = (45 kg × velocity of you (final)) + (9 kg × velocity of book (final))

Simplifying the equation:
90 kg·m/s = 45 kg × velocity of you (final) + 9 kg × velocity of book (final)

Since there is no friction, the final velocity of the book and your final velocity will be the same. Let's denote it as V.

90 kg·m/s = 45 kg × V + 9 kg × V

Combining like terms:
90 kg·m/s = (45 kg + 9 kg) × V

90 kg·m/s = 54 kg × V

Dividing both sides by 54 kg:
(Velocity of you (final)) = 90 kg·m/s ÷ 54 kg
(Velocity of you (final)) ≈ 1.67 m/s

Therefore, you will slide across the ice with a speed of approximately 1.67 m/s after throwing the book.