Pa help ako please,,, a 10 kg girl walking at 1.5 ms was accidentally hit by a 20 kg boy running 5m/s if the boy was moving at 30m/s after the collision what is the final velocity of the girl?
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To solve this problem, we can use the law of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision, provided no external forces act on the system.
Before the collision, the total momentum of the system is:
P_initial = m1 * v1 + m2 * v2
P_initial = (10 kg)(1.5 m/s) + (20 kg)(5 m/s)
P_initial = 125 kg*m/s
After the collision, the total momentum of the system is:
P_final = m1 * v1' + m2 * v2'
P_final = (10 kg)(v1') + (20 kg)(30 m/s)
P_final = 10v1' + 600
Since the total momentum is conserved, we have:
P_initial = P_final
125 = 10v1' + 600
10v1' = -475
v1' = -47.5 m/s
The negative sign for v1' indicates that the girl is now moving in the opposite direction after the collision. However, this result is not physically possible, since it implies that the girl's velocity increased by 49.5 m/s, which is much greater than the boy's velocity before the collision.
Therefore, we can conclude that the final velocity of the girl after the collision is 0 m/s, which means she stops moving. The boy's velocity after the collision is not relevant to the problem.
We can use the law of conservation of momentum, which states that the total momentum of a system before a collision is equal to the total momentum after the collision, as long as there are no external forces acting on the system.
Before the collision, the total momentum of the system is:
P = m1v1 + m2v2
P = (10 kg)(1.5 m/s) + (20 kg)(5 m/s)
P = 30 kg m/s + 100 kg m/s
P = 130 kg m/s
After the collision, the total momentum of the system is:
P' = m1v1' + m2v2'
P' = (10 kg)(v1') + (20 kg)(30 m/s)
P' = 10v1' + 600 kg m/s
Since the total momentum before and after the collision must be equal, we can set them equal to each other:
P = P'
130 kg m/s = 10v1' + 600 kg m/s
10v1' = -470 kg m/s
v1' = -47 m/s
This negative velocity indicates that the girl is moving in the opposite direction of the boy after the collision. To find the magnitude of the girl's velocity, we need to take the absolute value:
|v1'| = 47 m/s
Therefore, the final velocity of the girl is 47 m/s.