a 30 kg girl and a 25 kg boy face each other on a friction-free blades. The girl pushes the boy, who moves away at a speed of 1.0 m/s. The girls speed is __________m/s
To find the girl's speed, we can use the principle of conservation of momentum. Momentum is defined as the product of an object's mass and velocity, given by the equation:
Momentum = mass × velocity
According to the principle of conservation of momentum, the total momentum before the interaction is equal to the total momentum after the interaction, provided there are no external forces acting. In this case, the initial momentum of the system is zero because both the girl and the boy are initially at rest.
Let's use subscripts "g" for the girl and "b" for the boy to denote their respective masses and velocities.
Initial momentum, P_initial = P_g + P_b = 0
After the interaction, the boy moves away at a speed of 1.0 m/s. Therefore, the final velocity of the boy, v_b_final = 1.0 m/s.
Using the principle of conservation of momentum:
P_g + P_b = 0
(mass_g × velocity_g) + (mass_b × velocity_b) = 0
Substituting the given masses and boy's final velocity, we have:
(30 kg × velocity_g) + (25 kg × 1.0 m/s) = 0
Simplifying the equation further:
30 kg × velocity_g = -25 kg × 1.0 m/s
velocity_g = -25 kg × 1.0 m/s / 30 kg
Solving for velocity_g:
velocity_g ≈ -0.833 m/s
Given the context of this problem, the negative sign indicates that the girl is moving in the opposite direction of the boy. Therefore, the girl's speed is approximately 0.833 m/s in the opposite direction.