A 740 N student stands in the middle of a frozen pond having a radius of 4.8 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 2.8 kg physics textbook horizontally toward the north shore at a speed of 5.0 m/s. How long does it take him to reach the south shore?

Question

A 740 N student stands in the middle of a frozen pond having a radius of 4.8 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 2.8 kg physics textbook horizontally toward the north shore at a speed of 5.0 m/s. How long does it take him to reach the south shore?

Answer 1

To determine how long it takes for the textbook to reach the south shore, we can use the concept of projectile motion.

We need to consider two components of the textbook's motion: the horizontal component and the vertical component.

First, let's find the horizontal distance covered by the textbook. Since there is no friction, the horizontal velocity of the textbook remains constant throughout its flight. Therefore, we can use the equation:

distance = velocity * time

The horizontal distance covered is equal to the radius of the pond, which is 4.8 m.

4.8 m = 5.0 m/s * time

Now, let's solve this equation for time:

time = 4.8 m / 5.0 m/s
time ≈ 0.96 seconds

Hence, it takes the textbook approximately 0.96 seconds to reach the south shore of the pond.

Answer 2

To determine how long it takes for the student to reach the south shore, we need to calculate the time it takes for the textbook to reach the north shore.

We can start by calculating the initial horizontal velocity of the student after throwing the textbook. Since there is no friction between the student's shoes and the ice, the horizontal velocity of the student remains constant. Therefore, the initial horizontal velocity of the student is 5.0 m/s.

Next, we can calculate the horizontal distance between the student and the north shore using the radius of the pond. Since the student stands in the middle of the pond, the distance to the north shore is equal to half the circumference of the pond.

Circumference = 2 * π * radius
Circumference = 2 * 3.14 * 4.8 m
Circumference ≈ 30.144 m

Distance to north shore = 1/2 * Circumference
Distance to north shore ≈ 15.072 m

Now, we can calculate the time it takes for the student to reach the north shore using the formula:

Time = Distance / Velocity

Time = 15.072 m / 5.0 m/s
Time ≈ 3.0144 seconds

Therefore, it takes approximately 3.0144 seconds for the student to reach the north shore.