A 30kg girl and a 25 kg boy face each other on friction free roller blades the pushes the boy who moves away at a speed of 1.0m/s the girl's speed is m/s?
To find the girl's speed, we can use the principle of conservation of momentum. According to this principle, the total momentum before the push must be equal to the total momentum after the push.
Momentum is calculated by multiplying an object's mass by its velocity. Let's assign variables for the girl's and boy's masses (m1 = 30 kg, m2 = 25 kg) and velocities (v1 = girl's speed, v2 = boy's speed).
Before the push, the girl and the boy are stationary, so their initial momenta are both zero (0).
After the push, the boy moves away at a speed of 1.0 m/s. The girl moves in the opposite direction, so her velocity will be negative.
Using the conservation of momentum equation, we have:
(mass of girl * velocity of girl) + (mass of boy * velocity of boy) = 0
Substituting the given values:
(30 kg * v1) + (25 kg * 1.0 m/s) = 0
Simplifying the equation:
30 kg * v1 = -25 kg * 1.0 m/s
Dividing both sides by 30 kg:
v1 = (-25 kg * 1.0 m/s) / 30 kg
v1 ≈ -0.833 m/s
The girl's speed is approximately -0.833 m/s. The negative sign indicates that she is moving in the opposite direction of the boy.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before pushing should be equal to the total momentum after pushing.
The formula for momentum is:
Momentum = mass × velocity
Let's assign variables to the given values:
Mass of the girl (m₁) = 30 kg
Mass of the boy (m₂) = 25 kg
Initial velocity of the boy (v₂) = 1.0 m/s
Initial velocity of the girl (v₁) = ?
Using the principle of conservation of momentum, we have:
Initial momentum = Final momentum
(m₁ × v₁) + (m₂ × v₂) = (m₁ × v₁') + (m₂ × v₂')
Since the girl and the boy are facing each other, their initial velocities are in opposite directions. Therefore, the initial velocity of the girl is -v₁.
So, the equation becomes:
(m₁ × (-v₁)) + (m₂ × v₂) = (m₁ × v₁') + (m₂ × v₂')
Now, substituting the given values:
(30 kg × (-v₁)) + (25 kg × 1.0 m/s) = (30 kg × v₁') + (25 kg × 1.0 m/s)
Simplifying the equation:
-30v₁ + 25 = 30v₁ + 25
Combining like terms:
-30v₁ = 30v₁
Adding 30v₁ to both sides:
0 = 60v₁
Dividing both sides by 60:
0 = v₁
Therefore, the girl's speed after pushing is 0 m/s. She doesn't move in this case.