a person of mass 80 kg standing on a boat of mass 320 kg which at rest in still water the person is initially 12m from the shore the person walk on boat for 6 sec with a constant speed 1 m/s toward the shore and then stop distance of the person from the shore finally
The final distance of the person from the shore is 6 m.
To find the final distance of the person from the shore, we need to consider the conservation of momentum in this system.
Step 1: Calculate the initial momentum of the system.
The initial momentum of the system is zero since both the person and the boat are at rest.
Step 2: Calculate the final momentum of the system.
The final momentum of the system is also zero, as there is no net external force acting on the system.
Step 3: Apply the law of conservation of momentum.
According to the law of conservation of momentum, the initial momentum and the final momentum should be equal in an isolated system.
Initial Momentum = Final Momentum
0 = (Mass of the person × Velocity of the person) + (Mass of the boat × Velocity of the boat)
Step 4: Solve for the velocity of the boat.
Since the person's velocity is given (1 m/s) and the mass of the person and the boat are known, we can solve for the velocity of the boat.
0 = (80 kg × 1 m/s) + (320 kg × Velocity of the boat)
0 = 80 kg + 320 kg × Velocity of the boat
-80 kg = 320 kg × Velocity of the boat
Velocity of the boat = -80 kg / 320 kg
Velocity of the boat = -0.25 m/s
Note: The negative sign indicates that the boat is moving in the opposite direction of the person's walking movement.
Step 5: Calculate the distance covered by the boat.
The time and the velocity of the boat are given, so we can calculate the distance covered by the boat during the 6 seconds.
Distance covered by the boat = Velocity of the boat × Time
Distance covered by the boat = (-0.25 m/s) × 6 sec
Distance covered by the boat = -1.5 m
Note: The negative sign indicates that the boat has moved in the opposite direction from the shore.
Step 6: Calculate the final distance of the person from the shore.
Initially, the person was 12m from the shore, and during the time the person walked, the boat covered a distance of -1.5m. To find the final distance of the person from the shore, we need to subtract the distance covered by the boat from the initial distance.
Final distance of the person from the shore = Initial distance - Distance covered by the boat
Final distance of the person from the shore = 12 m - (-1.5 m)
Final distance of the person from the shore = 12 m + 1.5 m
Final distance of the person from the shore = 13.5 m
Therefore, the final distance of the person from the shore is 13.5 meters.
To find the final distance of the person from the shore, we need to consider the relative motion of the person with respect to the shore and the boat.
The initial distance of the person from the shore is 12m. The person then walks on the boat towards the shore with a constant speed of 1 m/s for 6 seconds. Therefore, the distance the person covers on the boat can be calculated as:
Distance covered on the boat = Speed × Time
= 1 m/s × 6 s
= 6 m
Now, we need to consider the movement of the boat as well. Since the person is walking on the boat, there will be a reaction force between the person and the boat. According to Newton's third law of motion, the reaction force will cause the boat to move in the opposite direction.
The mass of the person is 80 kg, and the mass of the boat is 320 kg. Therefore, the mass of the system (person + boat) is 80 kg + 320 kg = 400 kg.
As the boat and person are initially at rest in still water, the momentum of the system is zero. After the person walks on the boat, the boat starts moving in the opposite direction to maintain the momentum equilibrium.
According to the law of conservation of momentum, the momentum before the person starts walking is equal to the momentum after the person stops. Since the person's speed is constant, the change in momentum is equal to zero:
Change in momentum = Mass × (Final velocity - Initial velocity)
= 400 kg × (0 - 1 m/s)
= -400 kg · m/s
To maintain the conservation of momentum, the change in momentum of the system is transferred to the boat. Since the boat mass is 320 kg, we can calculate the velocity of the boat using the equation:
Change in momentum = Mass of boat × (Final velocity of boat - Initial velocity of boat)
-400 kg · m/s = 320 kg × (Final velocity of boat - 0)
Final velocity of boat = -400 kg · m/s / 320 kg
Final velocity of boat = -1.25 m/s
Now, we can calculate the distance covered by the boat in 6 seconds:
Distance covered by the boat = Speed × Time
= 1.25 m/s × 6 s
= 7.5 m
Finally, we can determine the final distance of the person from the shore by adding the distance covered on the boat to the initial distance from the shore:
Final distance from the shore = Initial distance from the shore + Distance covered on the boat
= 12 m + 7.5 m
= 19.5 m
Therefore, the final distance of the person from the shore is 19.5 meters.