A 0.14-kg baseball is dropped from rest from a height of 2.0 m above the ground.What is the magnitude of its momentum just before it hits the ground if we neglect air resistance?
A)0.28 kg ∙ m/s
B)0.88 kg ∙ m/s
C)0.44 kg ∙ m/s
D)0.62 kg ∙ m/s
E)1.4 kg ∙ m/s

Question

Quizplus · Accepted Answer

To find the momentum just before the baseball hits the ground, we first calculate its velocity using the formula derived from the conservation of energy: $v = \sqrt{2gh}$, where $g = 9.8 \, \text{m/s}^2$ is the acceleration due to gravity and $h = 2.0 \, \text{m}$ is the height. Plugging in the values, we get $v = \sqrt{2 \times 9.8 \times 2.0} = \sqrt{39.2} \approx 6.26 \, \text{m/s}$. The momentum $p$ is given by $p = mv$, where $m = 0.14 \, \text{kg}$ is the mass of the baseball. Thus, $p = 0.14 \times 6.26 \approx 0.8764 \, \text{kg} \cdot \text{m/s}$, which rounds to $0.88 \, \text{kg} \cdot \text{m/s}$, making option B the correct answer.

A 014-Kg Baseball Is Dropped from Rest from a Height of of 2.0