To get off a frozen frictionless lake, a 70.0 kg person takes off a 0.150 kg shoe and throws it horizontally directly away from the shore with a speed of 2.00 m/s. If the perrson is 5.00 m from the shore, how long does it take for her to reach it?
Her momentum after throwing will be equal and opposite to that of the shoe. Use that fact to get her velcoity V towards the shore.
V*70 kg= 0.150 kg * 2.00 m/s
Time = (5 meters)/V
To solve this problem, we can use the principle of conservation of momentum. The momentum before throwing the shoe will be equal to the momentum after throwing the shoe.
Step 1: Calculate the initial momentum before throwing the shoe.
The initial momentum of the person and the shoe is given by the product of their respective masses and velocities:
Initial momentum = (mass of person + mass of shoe) * velocity of person
Initial momentum = (70.0 kg + 0.150 kg) * 0 m/s (since the person is initially stationary)
Step 2: Calculate the final momentum after throwing the shoe.
The final momentum of the person and the shoe can be calculated separately:
Final momentum of the person = mass of person * velocity of person
Final momentum of the shoe = mass of shoe * velocity of shoe
Step 3: Apply the conservation of momentum.
According to the principle of conservation of momentum, the initial momentum should be equal to the final momentum:
Initial momentum = Final momentum of the person + Final momentum of the shoe
Step 4: Solve for the velocity of the person after throwing the shoe.
Since we are interested in the time it takes for the person to reach the shore, we need to solve for the final velocity of the person after throwing the shoe.
Final momentum of the person = mass of person * final velocity of the person
Step 5: Apply the equation of motion to calculate the time.
Using the equation of motion for horizontal motion, we can calculate the time it takes for the person to reach the shore. The equation is:
Distance = Velocity * Time
Rearranging the equation:
Time = Distance / Velocity
Now we can substitute the values into the equation to calculate the time it takes for the person to reach the shore.
Note: We are assuming that there are no external forces acting on the person that would affect their velocity.
Let's calculate the time it takes for the person to reach the shore:
Step 1: Calculate the initial momentum before throwing the shoe.
Initial momentum = (70.0 kg + 0.150 kg) * 0 m/s
Initial momentum = 70.150 kg * 0 m/s
Initial momentum = 0 kg·m/s
Step 2: Calculate the final momentum after throwing the shoe.
Final momentum of the person = 70.0 kg * final velocity of the person
Final momentum of the shoe = 0.150 kg * 2.0 m/s
Step 3: Apply the conservation of momentum.
0 kg·m/s = (70.0 kg * final velocity of the person) + (0.150 kg * 2.0 m/s)
Step 4: Solve for the velocity of the person after throwing the shoe.
70.0 kg * final velocity of the person = -0.150 kg * 2.0 m/s
final velocity of the person = (-0.150 kg * 2.0 m/s) / 70.0 kg
final velocity of the person = -0.0043 m/s
Step 5: Apply the equation of motion to calculate the time.
Time = distance / velocity
Time = 5.00 m / (-0.0043 m/s)
Time ≈ -1163.95 seconds
Since time cannot be negative, we can conclude that the person does not reach the shore.
Therefore, it is not possible for the person to reach the shore by throwing the shoe with the provided information.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the momentum before the person throws the shoe should be equal to the momentum after the shoe is thrown.
The momentum of an object can be calculated by multiplying its mass by its velocity. Let's denote the mass of the person as M and the velocity as V. The mass of the shoe is m, and its velocity after being thrown is v.
Initially, there is no momentum, as the person and the shoe are at rest. So, the initial momentum is zero: 0 = (M + m) * 0
After the shoe is thrown, the total momentum should still be zero, but now it is divided between the person and the shoe. The momentum of the person is given by M * V, and the momentum of the shoe is given by m * v:
0 = M * V + m * v
We can rearrange this equation to solve for the velocity of the shoe after being thrown:
m * v = -M * V
v = -M * V / m
Now we can use the equation of motion to calculate the time it takes for the shoe to reach the shore. The distance traveled by the shoe is 5.00 m, and its velocity is 2.00 m/s. The equation for distance traveled with constant velocity is:
distance = velocity * time
Rearranging this equation, we can solve for time:
time = distance / velocity
Substituting the values into the equation:
time = 5.00 m / 2.00 m/s = 2.50 seconds
Therefore, it takes 2.50 seconds for the shoe to reach the shore.