# Projectiles & air resistance?

1. Feb 15, 2005

### Physicist

Hi all,

If someone threw a ball vertically & we want to calculate the time needed to for the ball to return back to his hand taking into account air resistance, would it be different if we ignore air resistance??

When they derive the known laws for the maximum height, range & time, did they ignore air resistance?

Thanks

2. Feb 15, 2005

### FredGarvin

Yes. They do ignore wind resistance. The standard equations of motion that most people are familiar with deal with a constant acceleration. Wind resistance is not constant.

The amount of error induced is going to depend greatly on the gemoetry, displacemets and speeds involved. In your example of tossing a ball, the error induced by not taking into account drag would be much much less (probably an order of magnitude less) than if the ball was shot up thousands of feet and allowed to come back down. The speeds the ball would reach being thrown would not come close to the speeds it would reach if it fell from a thousand feet. Also consider the fact that if a ball were dropped from a sufficient height, the ball would eventually stop accelerating (due to drag) and would fall at a constant speed.

Also, consider what the equations would tell you if you calculated how long it would take a flat peice of paper to fall from some height. It wouldn't be even close because in that case wind resistance plays a huge role.

It is up to the person applying the equations to make the proper assumption as to whether or not neglecting a complex term is a proper assumption to make.

Maximum height, range and time of what?

3. Feb 24, 2005

### wizsid

generally the air resistance is proportional to the instantaneous velocity of the body.....so when u actually calculate the equation of motion it is exponential