Question

1. a 0.150-kg baseball is dropped from rest. if the magnitude of the baseball’s momentum is 0.780 kg m/s just before it lands on the ground, from what height was it dropped?

Answer 1

To determine the height from which a 0.150-kg baseball was dropped, given its momentum of 0.780 kg·m/s before landing, we use the momentum formula to find its velocity and then apply conservation of energy to calculate the height. The calculated height is approximately 1.38 meters.

Step-by-step explanation:

To find the height from which a 0.150-kg baseball was dropped given that its momentum is 0.780 kg·m/s just before it lands, we can use the conservation of mechanical energy and the formula for momentum.

The formula for momentum is:

p = m · v

Where:

p is the momentum

m is the mass of the object

v is the velocity of the object

We can rearrange the formula to solve for velocity (v):

v = p / m

Substituting the given numbers we find:

v = 0.780 kg·m/s / 0.150 kg

v = 5.2 m/s

Next, we use the conservation of mechanical energy. The potential energy (PE) at the height (h) will be converted into kinetic energy (KE) just before the ball hits the ground. The formula for kinetic energy is:

KE = 0.5 · m · v^2

Since the baseball was dropped from rest, its initial kinetic energy is 0, and all the potential energy would have been converted to kinetic energy at the point just before impact. Thus:

PE = KE

m · g · h = 0.5 · m · v^2

Where g is the acceleration due to gravity (9.8 m/s^2). We can cancel out the mass (m) since it appears on both sides, and solve for height (h):

h = (0.5 · v^2) / g

Substituting the known values:

h = (0.5 · (5.2 m/s)^2) / 9.8 m/s^2

h = 1.38 m

So, the baseball was dropped from a height of approximately 1.38 meters.

Answer 2

The baseball was dropped from a height of 0 meters.

Step-by-step explanation:

To find the height from which the baseball was dropped, we can use the equation for momentum.

Momentum = mass x velocity

Given that the mass of the baseball is 0.150 kg and the magnitude of its momentum just before it lands is 0.780 kg m/s, we can rearrange the equation to solve for the velocity.

0.780 kg m/s = 0.150 kg x velocity

Velocity = 0.780 kg m/s / 0.150 kg = 5.2 m/s

Since the baseball was dropped from rest, its initial velocity is 0 m/s. We can use the equation for acceleration due to gravity to determine the height from which the baseball was dropped.

Velocity² = Initial velocity² + 2 x acceleration x distance

0 = (0 m/s)² + 2 x 9.8 m/s² x distance

Distance = 0 / (2 x 9.8 m/s²) = 0 m

Therefore, the baseball was dropped from a height of 0 meters.