A 0.140-kg baseball is dropped from rest from a height of 2.00 m above the ground. What is the magnitude of its momentum just before it hits the ground?
A) 0.280 kg∙m/s
B) 0.877 kg∙m/s
C) 0.439 kg∙m/s
D) 0.620 kg∙m/s
E) 1.37 kg∙m/s

Question

Quizplus · Accepted Answer

We can use the conservation of energy and the fact that at the instant just before hitting the ground, all the potential energy will be converted to kinetic energy. Therefore:

mgh = (1/2)mv^2

where m is the mass of the baseball, g is the acceleration due to gravity, h is the height from which the ball was dropped, and v is the velocity just before hitting the ground.

Solving for v, we get:

v = sqrt(2gh)

Substituting the given values, we get:

v = sqrt(2 * 9.81 m/s^2 * 2.00 m) = 4.43 m/s

The momentum just before hitting the ground is given by:

p = mv = 0.140 kg * 4.43 m/s = 0.620 kg·m/s

Therefore, the best choice is B.

A 0140-Kg Baseball Is Dropped from Rest from a Height of of 2.00