(a) To find the momentum of the ball at its maximum height, we first need to know that at the maximum height, the velocity of the ball is 0 m/s. This is the point where the ball momentarily stops before falling back down.
Using the equation:
m₁v₁ = m₂v₂
where m₁v₁ is the initial momentum of the ball and m₂v₂ is the momentum of the ball at its maximum height.
Let's plug in the values we have:
m₁ = 0.100 kg (mass of the ball)
v₁ = 15.0 m/s
v₂ = 0 m/s
0.100 kg * 15.0 m/s = 0.100 kg * 0 m/s
1.50 kg m/s = 0,
So the momentum of the ball at its maximum height is 0.
(b) To find the momentum of the ball halfway up to its maximum height, we need to find the velocity of the ball at that point. Since we know the velocity is 0 m/s at the maximum height and assuming the velocity decreases uniformly, the velocity halfway up would be half of the initial velocity.
v = 15.0 m/s / 2
v = 7.50 m/s
Now, we can find the momentum at this point:
m₂v₂ = 0.100 kg * 7.50 m/s
m₂v₂ = 0.750 kg m/s
So the momentum of the ball halfway up to its maximum height is 0.750 kg m/s.
(7) A 0.100-kg ball is thrown straight up into the air with an initial speed of 15.0 m/s. Find the momentum of the
ball (a) at its maximum height and (b) halfway up to its maximum height
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