a 60 kg boy and a 40 kg girl at rest push off one another on some roller skates. if the speed of the guy is 5 m/s what is the speed of the female?
since you need to conserve momentum,
the boy has 3/2 the mass, so the girl has 3/2 the velocity
what does that mean
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the push-off should be equal to the total momentum after the push-off.
The momentum of an object is given by the product of its mass and velocity. Therefore, the momentum of the boy before the push-off is:
Momentum_boy_before = mass_boy * velocity_boy = 60 kg * 5 m/s = 300 kg·m/s.
Similarly, the momentum of the girl before the push-off is:
Momentum_girl_before = mass_girl * velocity_girl.
Since both the boy and the girl are initially at rest, the initial velocity of the girl is 0 m/s:
Momentum_girl_before = mass_girl * 0 m/s = 0 kg·m/s.
After the push-off, the boy and the girl move in opposite directions. Let's assume the speed of the girl after the push-off is v_girl. The speed of an object has a magnitude but no direction (as opposed to velocity). Therefore, the speed of the girl is the magnitude of her velocity.
The momentum of the boy after the push-off is:
Momentum_boy_after = mass_boy * velocity_boy = 60 kg * 5 m/s = 300 kg·m/s.
The momentum of the girl after the push-off is:
Momentum_girl_after = mass_girl * velocity_girl = mass_girl * v_girl.
According to the principle of conservation of momentum, the sum of the momenta before the push-off should be equal to the sum of the momenta after the push-off:
Momentum_boy_before + Momentum_girl_before = Momentum_boy_after + Momentum_girl_after.
Plugging in our known values:
300 kg·m/s + 0 kg·m/s = 300 kg·m/s + mass_girl * v_girl.
We can simplify this equation to:
0 kg·m/s = mass_girl * v_girl.
Since we know that the girl has a mass of 40 kg, we can now solve this equation to find the speed of the girl:
0 kg·m/s = 40 kg * v_girl.
Dividing both sides of the equation by 40 kg:
0 kg·m/s / 40 kg = v_girl.
Simplifying:
0 m/s = v_girl.
Therefore, the speed of the girl after the push-off is 0 m/s.