A boy throws a 4-kg pumpkin at 8 m/s to a 40-kg girl on roller skates, who catches it. At what speed does the girl then move backward?
*I don't understand how to work them*
Is the right answer .8m/s
To find the speed at which the girl moves backward after catching the pumpkin, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the interaction is equal to the total momentum after the interaction.
Momentum (p) is defined as the product of an object's mass (m) and its velocity (v). Mathematically, p = m * v.
Let's first calculate the momentum of the pumpkin before it is caught:
Momentum of the pumpkin = mass of the pumpkin * initial velocity of the pumpkin
= 4 kg * 8 m/s
Next, we calculate the momentum of the girl and the pumpkin combined after the interaction. Since the girl is initially at rest, her momentum is zero (mass * 0). Therefore, the total momentum after the interaction is only due to the pumpkin.
Since momentum is conserved, we equate the momentum before the interaction to the momentum after the interaction:
Momentum of the pumpkin before = Momentum of the pumpkin after
4 kg * 8 m/s = (mass of the pumpkin + mass of the girl combined) * final velocity of the girl.
To find the final velocity of the girl, we rearrange the equation and solve for v:
final velocity of the girl = (4 kg * 8 m/s) / (40 kg)
Now we can calculate the speed at which the girl moves backward by taking the magnitude of the final velocity:
Speed = |final velocity of the girl|
To reduce any confusion between speed and velocity, speed is always a positive quantity as it only tells us the magnitude of the velocity.
So, the speed at which the girl moves backward after catching the pumpkin can be calculated by dividing the momentum of the pumpkin before the interaction by the total mass of the girl and the pumpkin combined, and taking the positive value of the final velocity.