A 705 N man stands in the middle of a frozen pond of radius 4.0 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 4.0 m/s. How long does it take him to reach the south shore?

initial momentum North = 0

no external horizontal forces on system
therefore final momentum North = 0
0 = (705/9.8)V + 1.2 * 4
V is his speed north, it is negative so he goes south of course. I think you can do distance = rate * time

To solve this problem, we can use the principle of conservation of momentum. The momentum before throwing the textbook is equal to the momentum after throwing the textbook.

The momentum before throwing the textbook is zero since the man is not moving. The textbook will have a momentum after throwing it. Since the man is standing in the middle of the pond, the momentum after throwing the textbook must be equal to the momentum of the man and the textbook combined.

First, we need to calculate the momentum of the man and the textbook combined.

The momentum (p) is given by the formula: p = m * v

Where:
- p is the momentum
- m is the mass
- v is the velocity

The mass of the man is given as 705 N, and we need to convert it to kg by dividing it by the acceleration due to gravity, g.

mass (m) = 705 N / 9.8 m/s^2 = 71.94 kg (approximately)

The mass of the textbook is given as 1.2 kg.

The velocity of the textbook is given as 4.0 m/s.

Now, we can calculate the momentum of the man and the textbook combined.

momentum (p) = (mass of the man + mass of the textbook) * velocity

momentum (p) = (71.94 kg + 1.2 kg) * 4.0 m/s

momentum (p) = 73.14 kg * 4.0 m/s

momentum (p) = 292.56 kg m/s

Now, we can calculate the time taken for the man to reach the south shore. Since the man is unable to get to the other side due to the lack of friction, he will move in the opposite direction of the thrown textbook.

The distance from the center of the pond to the south shore is equal to the radius of the pond, which is 4.0 m.

To calculate the time, we can use the equation: t = d / v

Where:
- t is the time
- d is the distance
- v is the velocity

time (t) = 4.0 m / 4.0 m/s

time (t) = 1.0 s

Therefore, it will take the man 1.0 second to reach the south shore.