A 715 N man stands in the middle of a frozen pond of radius 10.0 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 10.0 m/s. How long does it take him to reach the south shore?
first find his mass in kilograms
m = 715 / 9.81
then use conservation of momentum
(total of 0 before the toss)
0 = (715/9.81) v - 1.2 * 10
solve for v
how long does it take to go 10 meters at v meters/second?
To determine how long it takes for the man to reach the south shore, we need to analyze the motion of the textbook.
Given:
- Mass of the man, m1 = 715 N (Note: The unit should be in kg, not N as N is the unit for force, not mass.)
- Mass of the textbook, m2 = 1.2 kg
- Initial speed of the textbook, v = 10.0 m/s
We can start by calculating the momentum of the textbook, which is the product of its mass and velocity:
Momentum (p) = m2 * v
Next, we need to consider the concept of conservation of momentum. Since there is no external force acting on the system (the man and the textbook), the total momentum before and after the throw remains constant.
Initially, the man is stationary, so the total momentum (p_total_initial) is only due to the textbook, which is given by:
p_total_initial = m2 * v
Finally, taking into account the man's mass, the total momentum (p_total_final) after the throw is given by:
p_total_final = (m1 + m2) * v_final
Since the man and textbook move together, the final velocity of the system (v_final) is the velocity of the man.
To find the time it takes for the man to reach the south shore, we can use the equation of motion:
distance = velocity * time
The distance travelled by the man is equal to the circumference of the pond, which is given by:
distance = 2 * π * radius
Now, we can rearrange the equation to solve for time:
time = distance / velocity (since distance = velocity * time)
Plugging in the values:
time = (2 * π * radius) / v_final
Substituting the value of v_final with the equation for momentum:
time = (2 * π * radius) / [(m1 + m2) * v_initial / m2]
Simplifying further:
time = (2 * π * radius * m2) / [(m1 + m2) * v_initial]
Now we can substitute the given values to find the time it takes for the man to reach the south shore.