A 755 N man stands in the middle of a frozen pond of radius 9.0 m. He is unable to get to the other side because of a lack of friction between his shoes and the ice. To overcome this difficulty, he throws his 1.2 kg physics textbook horizontally toward the north shore at a speed of 9.0 m/s. How long does it take him to reach the south shore?

I need this done step by step.

He has to travel 9.0 meters. Get his speed V after throwing the book by using the law of conservation of momentum.

You will need to convert the man's weight (in N) to his mass in kg, by dividing the weight by g.

Mbook*Vbook = Mman*V

1.2 * 9.0 = (755/g)* V = 77 V
V = 0.14 m/s

Time = distance/V = 9.0 m/0.14 m/s
= ___ s

To solve this problem, we need to use the concept of conservation of momentum.

1. First, let's calculate the initial momentum of the man and the textbook. Momentum is given by the equation p = mv, where p is momentum, m is mass, and v is velocity.

Momentum of the man: p_man = m_man * v_man
Momentum of the textbook: p_textbook = m_textbook * v_textbook

Given:
Mass of the man (m_man) = 755 N (we'll convert this to kg later)
Mass of the textbook (m_textbook) = 1.2 kg
Velocity of the textbook (v_textbook) = 9.0 m/s

To find the velocity of the man (v_man), we can use the conservation of momentum equation:

p_man + p_textbook = 0 (initial momentum is zero)

Rearranging the equation, we have:
m_man * v_man + m_textbook * v_textbook = 0

2. Now let's solve for the man's velocity (v_man):

v_man = (-m_textbook * v_textbook) / m_man

Plugging in the values:
v_man = (-1.2 kg * 9.0 m/s) / 755 N (N is a measure of force, not mass)

To convert the force from Newton to kg, we can use the equation:
1 N = 1 kg * 1 m/s^2

Therefore, 755 N = 755 kg * 1 m/s^2

Plugging in the converted mass value:
v_man = (-1.2 kg * 9.0 m/s) / (755 kg * 1 m/s^2)

Simplifying, we have:
v_man ≈ -0.014 m/s (approximate value, disregard the negative sign since it represents direction)

3. Now, let's calculate the time it takes for the man to reach the south shore of the pond. The key to this calculation is the fact that velocity is equal to displacement divided by time (v = d/t).

The displacement (d) is equal to the radius of the pond (9.0 m) since the man is throwing the book straight across.

Rearranging the equation, we have:
t = d / v

Plugging in the values:
t = 9.0 m / 0.014 m/s

Simplifying, we have:
t ≈ 642.9 s (approximately)

Therefore, it takes approximately 642.9 seconds (or about 10.7 minutes) for the man to reach the south shore of the pond.