A person of mass 60 kg is standing on a raft of mass 40kg in a lake. The distance of a person from bank is 30m. If a person starts running towards bank with velocity 10m/s then his distance from bank after 1s will be ?? And explain with diagram and proper steps
the distance of the and is 30m so if a person starts running towards the bank with a velocity of 10m/s then the distance of the bank will be 31 because you add the one second and then divide by your 10m/s
To find the distance of the person from the bank after 1 second, we need to consider the principle of conservation of momentum.
Step 1: Draw a diagram representing the situation.
```
Person (60 kg) Raft (40 kg)
//----------------------\\
< --- +
/ ---------------------- \\
```
The arrow indicates the direction of motion. The person is running towards the bank with a velocity of 10 m/s.
Step 2: Identify the initial momentum of the system.
The initial momentum of the system is given by:
Initial momentum = (mass of person * velocity of person) + (mass of raft * velocity of raft)
= (60 kg * 10 m/s) + (40 kg * 0 m/s)
= 600 kg·m/s + 0 kg·m/s
= 600 kg·m/s
Step 3: Use the conservation of momentum principle.
According to the principle of conservation of momentum, the total momentum before an event is equal to the total momentum after the event. Since no external forces are acting on the system, the initial momentum should be equal to the final momentum.
Step 4: Calculate the final momentum of the system.
Final momentum = (mass of person * velocity of person after 1 second) + (mass of raft * velocity of raft after 1 second)
Note that the person and the raft move together as a single system, so their final velocities will be the same.
Step 5: Apply the conservation of momentum.
By setting the initial momentum equal to the final momentum, we can solve for the velocity of the person (and hence, the raft) after 1 second.
600 kg·m/s = (60 kg * v) + (40 kg * v)
600 kg·m/s = 100 v + 40 v
600 kg·m/s = 140 v
Step 6: Solve for the velocity of the person (and raft) after 1 second.
v = 600 kg·m/s / 140 kg
v ≈ 4.286 m/s
Step 7: Calculate the distance of the person from the bank after 1 second.
Distance = initial distance - (velocity * time)
Distance = 30 m - (4.286 m/s * 1 s)
Distance ≈ 30 - 4.286
Distance ≈ 25.714 m
Therefore, the distance of the person from the bank after 1 second is approximately 25.714 meters.
To determine the person's distance from the bank after 1 second, we need to analyze the motion of the person and the raft separately.
Here are the steps to calculate the distance:
Step 1: Set up the diagram:
Draw a diagram with a point representing the person on the raft, another point representing the bank, and a labeled arrow indicating the direction towards the bank.
Step 2: Analyze forces on the raft:
Since the raft is on the water, it experiences an upward buoyant force and a downward gravitational force. As the raft is not accelerating vertically, the summation of these forces is zero:
Buoyant force = Gravitational force
B_raft = m_raft * g
where B_raft is the buoyant force, m_raft is the mass of the raft (40 kg), and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Step 3: Analyze forces on the person:
The person also experiences an upward buoyant force and a downward gravitational force. Additionally, there is a horizontal friction force acting on the person due to their motion on the raft. However, since the person is running towards the bank, the horizontal friction force is not relevant in determining their distance from the bank.
Step 4: Determine the net force on the person in the horizontal direction:
The net horizontal force on the person can be calculated by subtracting the friction force from the buoyant force:
Net horizontal force = Buoyant force - Friction force
Step 5: Apply Newton's second law in the horizontal direction:
According to Newton's second law, the net horizontal force is equal to the mass of the person multiplied by their acceleration:
Net horizontal force = m_person * a
where m_person is the mass of the person (60 kg) and a is their acceleration.
Step 6: Relate force, mass, and acceleration:
Equating the expressions for the net horizontal force from steps 4 and 5, we can solve for the person's acceleration:
m_person * a = B_person
where B_person represents the buoyant force acting on the person.
Step 7: Determine person's acceleration:
Substituting the expression for the buoyant force on the person, derived in a manner similar to step 2, we have:
m_person * a = m_person * g
Thus, the acceleration of the person is equal to the acceleration due to gravity (g).
Step 8: Apply the first equation of motion:
Now, using the first equation of motion, we can calculate the distance traveled by the person after 1 second:
distance = initial velocity * time + 0.5 * acceleration * time^2
Since the initial velocity is 10 m/s and the time is 1 second, plugging in these values, we get:
distance = 10 * 1 + 0.5 * 9.8 * 1^2
After simplification, the person's distance from the bank after 1 second will be:
distance = 10 + 0.5 * 9.8
Therefore, the person's distance from the bank after 1 second will be 14.9 meters.