solving for time

[GASPER20]

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Since total time of a flight can be solved either by:

t = 2v/g or t = (2d/g)^1/2 when Vo is zero,

if we decrease gravity by a factor 3, will time increase by a factor of 3 or 3^1/2?

thanks

 

[addo]

Since total time of a flight can be solved either by:

t = 2v/g or t = (2d/g)^1/2 when Vo is zero,

if we decrease gravity by a factor 3, will time increase by a factor of 3 or 3^1/2?

thanks

a=g
a=v/t=2d/t^2=tv=2d
t=2d/v
v=at
t=2d/at
t^2=2d/a
I think when you want to change a by some factor, you must square t to for the two expressions to be equal....otherwise they wouldnt, but they really are, so if you decrease gravity, time will increase by a factor of 3. If you increase time by a factor of 3, then velocity increases by a factor of 3, and decreases time by a factor of 3....so equation
t=2d/v would be valid....or not... sounds like you know the answer, im really curious now.

 

[BerkReviewTeach]

Since total time of a flight can be solved either by:

t = 2v/g or t = (2d/g)^1/2 when Vo is zero,

if we decrease gravity by a factor 3, will time increase by a factor of 3 or 3^1/2?

thanks

When you change g, the maximum height the object reaches changes, so the second equation has two variables that are changing. You'd need to plug in a new value for g and d, which makes that equation difficult to use. It will eventually match the result of the first equation, but requires more work.

If you are launching at the same initial velocity, then the first equation is the easier one to use. If g decreases by a factor of 3, then the flight time increases by a factor of 3.

 

[GASPER20]

When you change g, the maximum height the object reaches changes, so the second equation has two variables that are changing. You'd need to plug in a new value for g and d, which makes that equation difficult to use. It will eventually match the result of the first equation, but requires more work.

If you are launching at the same initial velocity, then the first equation is the easier one to use. If g decreases by a factor of 3, then the flight time increases by a factor of 3.

thanks for the input!

@addo
the answer to my hypothetical problem is:
time increases by 3 if g decreases by 3