- #1
nicholaslyz
- 1
- 0
Hi,
I was wondering in my physics class the other day, whether if you throw up a ball from a height say h with velocity v0 , facing air resistance Fair=-bv on its way up and down, would it reach its initial height h again faster or slower than if you were to throw it up in a vacuum (i.e. Fair=0)?
It's hideously complicated...for starters the time taken for the ball to reach its maximum height in the presence of air resistance is [tex]t =- \frac{m}{b}\ln \frac{1}{1+\frac{bv_0}{gm}}[/tex]
You can check this by [tex]\lim_{b \to 0}\Big(\textstyle \frac{-m}{b} \ln \frac{1}{1+\frac{bv_0}{gm}}\Big)=\frac{v_0}{g}[/tex] , so if b = 0 then the equation is the one for time taken to reach the maximum height in vacuum.
So does the ball rise and fall faster in air resistance?
I was wondering in my physics class the other day, whether if you throw up a ball from a height say h with velocity v0 , facing air resistance Fair=-bv on its way up and down, would it reach its initial height h again faster or slower than if you were to throw it up in a vacuum (i.e. Fair=0)?
It's hideously complicated...for starters the time taken for the ball to reach its maximum height in the presence of air resistance is [tex]t =- \frac{m}{b}\ln \frac{1}{1+\frac{bv_0}{gm}}[/tex]
You can check this by [tex]\lim_{b \to 0}\Big(\textstyle \frac{-m}{b} \ln \frac{1}{1+\frac{bv_0}{gm}}\Big)=\frac{v_0}{g}[/tex] , so if b = 0 then the equation is the one for time taken to reach the maximum height in vacuum.
So does the ball rise and fall faster in air resistance?