A 30 kg girl and a 25 kg boy face each other on friction-free roller blades. The girl pushes the boy, who moves away at a speed of 1.0 m/s. The girl speed is _______ m/s?
The girl's momentum is equal and of opposite sign, so the total momentum remains zero.
30*Vgirl = 25*1.0
Solve for Vgirl
0.83 m/s
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the initial momentum of a system is equal to the final momentum of the system.
The momentum of an object is calculated by multiplying its mass by its velocity: momentum = mass × velocity.
Let's denote the girl's speed as v. Initially, both the girl and the boy are at rest, so their initial momentum is zero.
Initial momentum = (mass of girl × velocity of girl) + (mass of boy × velocity of boy)
Since the girl pushes the boy, the final momentum of the system is given by:
Final momentum = 0 (since both girl and boy have opposite velocities)
According to the principle of conservation of momentum:
Initial momentum = Final momentum
(30 kg × 0) + (25 kg × 0) = (30 kg × v) + (-25 kg × 1.0 m/s)
0 = 30 kg × v - 25 kg
25 kg = 30 kg × v
To find the girl's speed, v, we can rearrange the equation as follows:
v = 25 kg ÷ 30 kg
v ≈ 0.833 m/s
Therefore, the girl's speed is approximately 0.833 m/s.
To find the speed of the girl, we can apply the conservation of momentum.
The total momentum before the push is equal to the total momentum after the push. Momentum is defined as the product of mass and velocity.
Let's assume the initial velocity of the girl is 'v'.
The momentum before the push:
Girl's momentum = mass of the girl × velocity of the girl
Boy's momentum = mass of the boy × velocity of the boy (which is 0 since he is initially at rest)
Therefore, the total momentum before the push = (mass of the girl × velocity of the girl) + (mass of the boy × 0)
Total momentum before the push = mass of the girl × velocity of the girl
The total momentum after the push:
Girl's momentum = mass of the girl × final velocity of the girl, which is what we need to find.
Boy's momentum = mass of the boy × velocity of the boy
Therefore, the total momentum after the push = (mass of the girl × final velocity of the girl) + (mass of the boy × velocity of the boy)
According to the conservation of momentum, the total momentum before the push is equal to the total momentum after the push.
mass of the girl × velocity of the girl = (mass of the girl × final velocity of the girl) + (mass of the boy × velocity of the boy)
Substituting the given values:
30 kg × v = (30 kg × final velocity of the girl) + (25 kg × 1.0 m/s)
Now we can solve for the final velocity of the girl.
30 kg × v = 30 kg × final velocity of the girl + 25 kg × 1.0 m/s
30v = 30(final velocity of the girl) + 25
Simplifying the equation:
30v - 30(final velocity of the girl) = 25
30(final velocity of the girl) = 30v - 25
(final velocity of the girl) = (30v - 25) / 30
Therefore, the speed of the girl is (30v - 25) / 30 m/s.