A boy throws a 4-kg pumpkin at 8m/s to a 40kg girl on roller skates, who catches it. At what speed does the girl then move backwards?
Assume the girl was facing the boy, and was stationary before catching the pumpkin.
Her initial momentum is zero.
Momentum of the punmkin
= 4 kg * 8 m/s
= 32 kg-m/s
Combined mass of girl and pumpkin
= 4+40
= 44 kg
Final velocity
= 32 kg-m-s-1 / 44 kg
= 8/11 m/s
Well, this sounds like quite the hilarious scenario! So, we have a boy throwing a 4kg pumpkin at 8m/s to a 40kg girl on roller skates. Let's calculate what happens next.
To do that, we need to apply what's called the law of conservation of momentum. According to this law, the total momentum before the pumpkin is caught should be equal to the total momentum after the catch.
The momentum before the catch can be calculated by multiplying the mass of the pumpkin (4kg) by its initial velocity (8m/s), which gives us a momentum of 32 kg·m/s.
Since the pumpkin is caught by the girl, her momentum after the catch should be equal and opposite to the momentum of the pumpkin. We can rearrange this equation to find the girl's velocity:
Girl's momentum = Pumpkin's momentum = 32 kg·m/s
After rearranging, we find:
Girl's velocity = Girl's momentum / Girl's mass
Plugging in the values, we get:
Girl's velocity = 32 kg·m/s / 40kg
And simplifying this, we find that the girl moves backward at a speed of 0.8 m/s.
So, to sum it up, when the girl catches the pumpkin, she moves backward at a speed of 0.8 m/s. I hope this explanation puts a smile on your face!
To find the speed at which the girl moves backward after catching the pumpkin, we can use the principle of conservation of momentum. According to this principle, the total momentum before and after the interaction should be the same.
The momentum of an object is calculated by multiplying its mass by its velocity.
Given:
Mass of the pumpkin, m1 = 4 kg
Initial velocity of the pumpkin, u1 = 8 m/s
Mass of the girl, m2 = 40 kg
Let's assume the final velocity of the girl with the pumpkin is v2.
Step 1: Calculate the momentum of the pumpkin before the interaction (initial momentum).
Momentum of the pumpkin, p1 = m1 * u1
Step 2: Apply the conservation of momentum.
Since there are no external forces acting on the system, the total momentum before and after the interaction remains the same.
Initial momentum = Final momentum
p1 = (m1 * u1) = (m1 + m2) * v2
Step 3: Solve for v2.
v2 = (m1 * u1) / (m1 + m2)
Using the values given, we can substitute them into the equation and calculate the velocity.
v2 = (4 kg * 8 m/s) / (4 kg + 40 kg)
v2 = (32 kg·m/s) / (44 kg)
v2 ≈ 0.73 m/s
Therefore, the girl moves backward at a speed of approximately 0.73 m/s after catching the pumpkin.
To determine the speed at which the girl moves backwards after catching the pumpkin, we can apply 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, provided there are no external forces acting on the system.
The momentum of an object is given by the product of its mass and velocity. Therefore, we can calculate the initial momentum of the pumpkin and the final momentum of the girl.
Given:
Mass of the pumpkin (m1) = 4 kg
Initial velocity of the pumpkin (v1) = 8 m/s
Mass of the girl (m2) = 40 kg
Final velocity of the girl (v2) = ?
First, calculate the momentum of the pumpkin (m1 * v1):
Momentum of the pumpkin (p1) = 4 kg * 8 m/s = 32 kg*m/s
Next, apply the conservation of momentum principle:
Initial momentum = Final momentum
p1 + 0 = 0 + p2
32 kg*m/s + 0 = 0 + (40 kg * v2)
Since the girl catches the pumpkin, the initial momentum is zero. Solving for v2, the final velocity of the girl:
40 kg * v2 = -32 kg*m/s
v2 = -32 kg*m/s / 40 kg
Therefore, the girl moves backwards at a speed of -0.8 m/s. The negative sign indicates the direction of motion, which in this case is opposite to the initial direction of the pumpkin's velocity.