When you hit a 0.27kg volleyball the contact time is 50ms and the average force is 125N.
If you serve the volleyball (from rest) sending it up at 30 degrees above the horizontal, what are the horizontal and vertical components of the momentum of the volleyball in kgm/s?
To find the horizontal and vertical components of momentum, we first need to find the total momentum of the volleyball. We can use the formula:
p = mv
where p is momentum, m is mass, and v is velocity.
Since the volleyball is initially at rest, its initial momentum is zero. We need to find its final momentum after it is hit.
To do this, we can use the impulse-momentum theorem, which states that:
Impulse = change in momentum
The impulse is given by:
Impulse = FΔt
where F is the average force and Δt is the contact time.
Substituting the given values, we get:
Impulse = 125 N * 0.05 s = 6.25 Ns
The change in momentum is equal to the final momentum minus the initial momentum. Since the initial momentum is zero, the final momentum is simply equal to the impulse:
p = 6.25 Ns
Now we can find the horizontal and vertical components of momentum. The horizontal component is given by:
p_h = p * cosθ
where θ is the angle above the horizontal. Substituting the given values, we get:
p_h = 6.25 Ns * cos30° = 5.41 kgm/s
The vertical component is given by:
p_v = p * sinθ
Substituting the given values, we get:
p_v = 6.25 Ns * sin30° = 3.13 kgm/s
Therefore, the horizontal component of momentum is 5.41 kgm/s and the vertical component of momentum is 3.13 kgm/s.