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,s speed is _ m/s.
To find the girl's speed, we can use the concept of conservation of momentum. According to this principle, the total momentum before the girl pushes the boy is equal to the total momentum after she pushes him.
The formula for momentum is given by the product of an object's mass and velocity:
Momentum = Mass × Velocity
Before the girl pushes the boy, both of them are at rest, so their initial momenta are zero:
Initial momentum of the girl = 0
Initial momentum of the boy = 0
After the girl pushes the boy, his momentum is given as:
Momentum of the boy = Mass of the boy × Velocity of the boy
Since the boy moves away at a speed of 1.0 m/s, we can substitute the given values into the equation:
Momentum of the boy = 25 kg × 1.0 m/s
Momentum of the boy = 25 kg × m/s
Now, according to the principle of conservation of momentum, the total initial momentum should equal the total final momentum:
Initial momentum of the girl + Initial momentum of the boy = Final momentum of the girl + Final momentum of the boy
Since the initial momentum of both the girl and the boy is zero, the equation becomes:
0 + 0 = Final momentum of the girl + 25 kg × m/s
Since the girl and the boy are facing each other, the direction of their momenta is opposite. Therefore, the velocity of the girl after she pushes the boy will be in the opposite direction, which we can represent as -v_girl.
-25 kg × m/s = -30 kg × (-v_girl)
Simplifying the equation, we have:
25 kg × m/s = 30 kg × v_girl
Dividing both sides of the equation by 30 kg:
(25 kg × m/s) / 30 kg = v_girl
Simplifying further, we get:
v_girl = (25/30) m/s
v_girl = 0.833 m/s (rounded to three decimal places)
So, the girl's speed after pushing the boy is approximately 0.833 m/s.