A boy moves on a skateboard at a constant velocity of 3m.s . The combined mass of the boy and the skateboard is 40kg. He catches a bag of flour of mass 5kg that is thrown to him horizontally at 6m.s . Determine the velocity of the boy after catching the bag of flour.
I don't know the answer
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To determine the velocity of the boy after catching the bag of flour, we need to use the principle of conservation of momentum. In this case, momentum is conserved because there are no external forces acting on the boy and the bag of flour in the horizontal direction.
The momentum of an object is defined as the product of its mass and velocity. Mathematically, it is given by:
Momentum = mass × velocity
According to the principle of conservation of momentum, the total momentum before the catch is equal to the total momentum after the catch. So, we can write the equation as:
Initial momentum = Final momentum
The initial momentum is the momentum of the boy before catching the bag of flour, and the final momentum is the momentum of the boy and the bag of flour combined after the catch.
Initial momentum of the boy = mass of the boy × velocity of the boy
Initial momentum of the bag of flour = mass of the bag of flour × velocity of the bag of flour
Final momentum of the boy and the bag of flour = total mass × final velocity
Now, let's substitute the values given in the question:
Mass of the boy = 40 kg
Velocity of the boy = 3 m/s
Mass of the bag of flour = 5 kg
Velocity of the bag of flour = 6 m/s
Initial momentum of the boy = 40 kg × 3 m/s
Initial momentum of the bag of flour = 5 kg × 6 m/s
Final momentum of the boy and the bag of flour = (40 kg + 5 kg) × final velocity
Now, we can set up the equation for conservation of momentum:
40 kg × 3 m/s + 5 kg × 6 m/s = (40 kg + 5 kg) × final velocity
Simplifying the equation:
120 kg m/s + 30 kg m/s = 45 kg × final velocity
150 kg m/s = 45 kg × final velocity
final velocity = 150 kg m/s / 45 kg
final velocity ≈ 3.33 m/s
Therefore, the velocity of the boy after catching the bag of flour is approximately 3.33 m/s.
from behind, or from in front of him?
In any case, just make sure the momentum before and after the catch is the same.