Buffy is rolling along in her 11.1 kg wagon at 4.6 m/s (in the positive direction) when she jumps off the back. She continues to move forward at 1.5 m/s relative to the ground. This causes her wagon to go speeding forward at 13.03 m/s relative to the ground. How much does Buffy weigh?
To find out how much Buffy weighs, we can use the principle of conservation of momentum.
The initial momentum of the system (Buffy + wagon) is equal to the final momentum of the system, according to the law of conservation of momentum.
The momentum (p) is calculated by multiplying the mass (m) by the velocity (v):
p = m * v
Let's denote the mass of Buffy as m1 (unknown), the mass of the wagon as m2 (given as 11.1 kg), and the initial velocity of the system as v1 (given as 4.6 m/s in the positive direction). After Buffy jumps off, the final velocity of the system is denoted as v2 (given as 13.03 m/s in the positive direction), and Buffy's velocity relative to the ground is denoted as v3 (given as 1.5 m/s in the positive direction).
Before Buffy jumps off:
Initial momentum = (m1 + m2) * v1
After Buffy jumps off:
Final momentum = m2 * v2 + m1 * v3
Since the momentum must be conserved, we can set the initial momentum equal to the final momentum:
(m1 + m2) * v1 = m2 * v2 + m1 * v3
Now we can substitute the given values into the equation:
(unknown weight + 11.1 kg) * 4.6 m/s = 11.1 kg * 13.03 m/s + unknown weight * 1.5 m/s
Simplifying the equation, we can now solve for the unknown weight:
(unknown weight + 11.1 kg) * 4.6 m/s - unknown weight * 1.5 m/s = 11.1 kg * 13.03 m/s
(4.6 m/s - 1.5 m/s) * unknown weight + (11.1 kg * 4.6 m/s - 11.1 kg * 13.03 m/s) = 0
3.1 m/s * unknown weight + 1.1 kg * 11.1 m/s = 0
Now, solve for the unknown weight:
3.1 m/s * unknown weight = -1.1 kg * 11.1 m/s
unknown weight = (-1.1 kg * 11.1 m/s) / 3.1 m/s
unknown weight ≈ -3.96 kg
The negative sign indicates that Buffy is exerting a force in the opposite direction, which is not physically possible in this situation. Therefore, we can discard the negative sign and take the magnitude of the weight:
Weight of Buffy ≈ 3.96 kg
Please note that this solution assumes constant mass and neglects other factors such as air resistance.
To find out how much Buffy weighs, we need to use the principle of conservation of momentum. The initial momentum of the system (Buffy + wagon) before Buffy jumps off is equal to the final momentum of the system after she jumps off.
The initial momentum of the system is given by:
Initial momentum = (mass of Buffy + mass of wagon) * initial velocity of the system
The final momentum of the system is given by:
Final momentum = mass of wagon * final velocity of the wagon
According to the principle of conservation of momentum, these two values are equal. Therefore, we can set up the equation:
(mass of Buffy + mass of wagon) * initial velocity of the system = mass of wagon * final velocity of the wagon
Let's solve the equation for the mass of Buffy (since we are trying to find her weight). We can rearrange the equation and solve for the mass of Buffy as follows:
mass of Buffy = (mass of wagon * final velocity of the wagon - mass of wagon * initial velocity of the system) / initial velocity of the system
Plugging in the given values:
mass of Buffy = (11.1 kg * 13.03 m/s - 11.1 kg * 4.6 m/s) / 4.6 m/s
Simplifying the equation:
mass of Buffy = 13.03 kg - 11.1 kg = 1.93 kg
Therefore, Buffy weighs approximately 1.93 kg.