An 80 kg hunter gets a rope around a 400 kg
polar bear. They are stationary and on frictionless
level ice, initially 60 m apart.
When the hunter pulls the polar bear to
him, the polar bear will move:
1. 10 m
2. 30 m
An 80 kg hunter gets a rope around a 400 kg
polar bear. They are stationary and on frictionless
level ice, initially 60 m apart.
When the hunter pulls the polar bear to
him, the polar bear will move:
1. 10 m
2. 30 m
Why?
To determine how far the polar bear will move when the hunter pulls it towards him, we need to consider conservation of momentum.
The initial momentum of the hunter and the polar bear is zero because they are stationary. When the hunter pulls the polar bear towards him, the conservation of momentum states that the total momentum of the system (hunter + polar bear) will remain constant.
The momentum of an object is given by the product of its mass and velocity (momentum = mass * velocity). Since the initial momentum is zero, the final momentum of the hunter and the polar bear must also be zero.
Let the distance the polar bear moves be x meters.
The hunter has a mass of 80 kg, and the polar bear has a mass of 400 kg. After the pull, the hunter and the polar bear move together. So, their velocities will be the same, and we can denote their common velocity as v.
The total momentum before the pull is given by:
Initial momentum = (mass of hunter * 0) + (mass of polar bear * 0) = 0
The total momentum after the pull is given by:
Final momentum = (mass of hunter * v) + (mass of polar bear * v) = 0
Since the factor v is common to both terms in the final momentum equation, we can rewrite it as:
v * (mass of hunter + mass of polar bear) = 0
Substituting the known values:
v * (80 kg + 400 kg) = 0
v * 480 kg = 0
To solve for v, we divide both sides by 480 kg:
v = 0 / 480 kg
v = 0 m/s
This means that the final velocity of the hunter and the polar bear is zero.
Now we can calculate how far the polar bear moves in the process. We know that the hunter initially is 60 meters away from the polar bear and that they end up at the same spot after the pull. Therefore, the distance the polar bear moves is equal to the initial separation between them, which is:
Distance = 60 m
Therefore, the polar bear will move 60 meters when the hunter pulls it towards him.
So the correct answer is not among the options provided.