A 70.8 kg man is standing on a frictionless ice surface when he throws a 2.3 kg book at 10.5 m/s. With what speed does the man move across the ice as a result?
no speed, if he throws it straight up.
Steve, you are an idiot. A physics problem and why would you assume he threw up. No answer is easy like that.
To find the speed at which the man moves across the ice, we can apply the law of conservation of momentum. According to this principle, the total momentum before the book is thrown should be equal to the total momentum after.
The momentum of an object is calculated by multiplying its mass by its velocity. Let's denote the man's velocity after throwing the book as v (which is what we want to find), and the initial velocity of the book as u.
The momentum of the man before throwing the book is given by:
Momentum_man_before = (mass of man) * (velocity of man before) = (70.8 kg) * (0 m/s) = 0 kg·m/s.
The total momentum before throwing the book is then:
Total_momentum_before = Momentum_man_before + Momentum_book_before
= 0 kg·m/s + (mass of book) * (velocity of book before)
= 0 kg·m/s + (2.3 kg) * (0 m/s)
= 0 kg·m/s.
According to the law of conservation of momentum, the total momentum before and after throwing the book should be equal. Therefore:
Total_momentum_before = Total_momentum_after.
When the man throws the book, he gains momentum in the opposite direction, causing him to move across the ice. Since the book's momentum after throwing is given by (mass of book) * (final velocity of book), the total momentum after becomes:
Total_momentum_after = Momentum_man_after + Momentum_book_after
= (mass of man) * (velocity of man after) + (mass of book) * (final velocity of book)
= (70.8 kg) * (v) + (2.3 kg) * (-10.5 m/s) (negative sign for the book's velocity as it moves in the opposite direction)
We equate the total momentum before and after to solve for v:
Total_momentum_before = Total_momentum_after
0 kg·m/s = (70.8 kg) * (v) + (2.3 kg) * (-10.5 m/s)
Now we can solve for v:
0 = 70.8v - 2.3 * 10.5
Rearranging and solving for v, we get:
70.8v = 24.15
v ≈ 0.34 m/s
Therefore, the man moves across the ice at a speed of approximately 0.34 m/s after throwing the book.