A boy on roller blades throws a jug of water away from himself, giving it a speed of 10 m/s. The boy's mass is 50 kg and the mass of the jug and water is 9 kg. What is the velocity gained by the boy?
momentum is conserved.
initialmomentum=finalmomentum
0=9(10)+50V
solve for V. Notice its direction (sign).
To answer this question, we need to use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, as long as no external forces are acting on the system.
In this case, we can consider the boy and the jug of water as a system, and we can calculate their total momentum both before and after the event to find the velocity gained by the boy.
The initial momentum of the system is given by the equation:
Initial momentum = (mass of the boy) × (initial velocity of the boy) + (mass of the jug and water) × (initial velocity of the jug and water)
Substituting the given values:
Initial momentum = (50 kg) × (0 m/s) + (9 kg) × (-10 m/s) (Note: Since the jug and water are thrown away, their initial velocity will be opposite to that of the boy, hence the negative sign)
Simplifying, the initial momentum is 0 kg⋅m/s, as the initial velocity of the boy is 0 m/s.
The final momentum of the system is given by the equation:
Final momentum = (mass of the boy) × (final velocity of the boy) + (mass of the jug and water) × (final velocity of the jug and water)
Since the jug and water are thrown away, their final velocity will be opposite to that of the boy. Let's assume the final velocity of the boy is v (to be determined).
Final momentum = (50 kg) × (v) + (9 kg) × (-10 m/s)
The conservation of momentum principle tells us that the initial momentum is equal to the final momentum, so we can set up an equation:
Initial momentum = Final momentum
0 kg⋅m/s = (50 kg) × (v) + (9 kg) × (-10 m/s)
Simplifying, we have:
0 = 50v - 90
Rearranging the equation, we get:
50v = 90
v = 90/50
v = 1.8 m/s
Therefore, the velocity gained by the boy is approximately 1.8 m/s.