Question

If an object is thrown straight up and air resistance is negligible, then its speed when it returns to the starting point is the same as when it was released. If air resistance were not negligible, how would its speed upon return compare with its initial speed? How would the maximum height to which it rises be affected?

Short answer

The air resistance force is inherently non-conservative, acting in the opposite direction of velocity.

Step-by-step solution

Nature of air resistance

The air resistance force is non-conservative in nature, acting in the opposing direction of velocity as the item is moving upward or downward.

As a result, air resistance conducts negative work and drains the object's energy.

As a result, the item returns to the starting position at a slower speed than before.

It won’t reach the maximum height if air resistance is present

Similarly, when the item rises, the air resistance drains the energy, resulting in a lower maximum height achieved than if there was no air resistance.

Wind resistance exists, and it works against the object in the opposite direction of the airflow (opposite direction of object velocity).

As a result, the object is pulled downward by both gravity and wind resistance as it climbs.

According to Newton's second law, the combined forces generate a downward acceleration greater than 1g.

On the way down, gravity still acts downward, but wind resistance acts upward since the object's velocity has reversed.

As a result, the total forces create less than 1g of downward acceleration.

You may also look at the condition of wind resistance using energy conservation.

Because wind resistance consumes energy during the object's flight, you may anticipate the object to have less mechanical energy when it returns to the bat at the end of the journey than it had at the start.

Because the object's mechanical energy is kinetic at both the beginning and conclusion of its flight, it must travel slower at the end than it did at the beginning.

That's only possible if the average acceleration along the journey is high enough.