A 750.0 N man, carrying a 1.9 kg physics textbook, stands at the center 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 his difficulty, he throws his textbook horizontally at a speed of 7.0 m/s toward the north shore. How long (in s) does it take him to reach the south shore?

Question

A 750.0 N man, carrying a 1.9 kg physics textbook, stands at the center 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 his difficulty, he throws his textbook horizontally at a speed of 7.0 m/s toward the north shore. How long (in s) does it take him to reach the south shore?

Answer 1

To find out how long it takes for the man to reach the south shore, we need to analyze the motion of the textbook.

Given:
Weight of the man (W) = 750.0 N
Mass of the textbook (m) = 1.9 kg
Radius of the frozen pond (r) = 9.0 m
Speed of the textbook (v) = 7.0 m/s

First, let's calculate the force with which the man throws the textbook. The force needed to throw the textbook horizontally is equal to the force required to accelerate it horizontally. This force will be equal to the frictional force between the man's shoes and the ice, which is given by the formula:

Frictional force (Ff) = coefficient of friction (µ) × normal force (N)

Since there is no friction between the man's shoes and the ice, the frictional force is zero. Therefore, the horizontal force with which the man throws the textbook is also zero.

Now, let's analyze the motion of the textbook after being thrown:

1. Horizontal Motion:
Since there is no horizontal force acting on the textbook, it will continue to move horizontally with a constant velocity of 7.0 m/s.

2. Vertical Motion:
The vertical motion of the textbook is affected by the force of gravity. The weight of the textbook creates a downward force (mg) where g is the acceleration due to gravity which is approximately 9.8 m/s².

Now, let's calculate the time it takes for the man to reach the south shore:

1. Vertical Motion:
The textbook is thrown horizontally, so its vertical motion is not directly related to the man's motion. Therefore, we can ignore the textbook's vertical motion.

2. Horizontal Motion:
Since the man is throwing the textbook horizontally, the horizontal displacement of the textbook (d) will be equal to the circumference of the pond (2πr):

d = 2πr = 2 × 3.14 × 9.0 m ≈ 56.52 m

The time taken for the textbook to cover this distance can be calculated using the formula:

Time (t) = Distance (d) / Velocity (v)

t = 56.52 m / 7.0 m/s ≈ 8.08 s

Therefore, it will take approximately 8.08 seconds for the man to reach the south shore.