EK Physics #96

[ayocaptain628]

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This is for the 1001 series
I don't understand the answer explanation given.
I understand that air resistance slows the projectile to a smaller max. height and shorter range, but I don't understand the time explanation.
Can someone explain the answer to me in better wording
I don't understand conceptually how time is still shortened

 

[Cawolf]

I don't have the book but can possibly offer you a decent explanation if you get a chance to post the question.

 

[ayocaptain628]

I don't have the book but can possibly offer you a decent explanation if you get a chance to post the question.

Ty!
The question is from EK Physics #1001 series
if you could possibly explain the answer key differently, that would be great
or if you have a much better explanation that helps u that would be great too

96. Air resistance would decrease all of the following EXCEPT
A. R (range)
B. h (height)
C. v (initial velocity)
D. t (time)

ans was C
solutions manual said: [in white]
b/c "initial velocity v is a given .:. not affected by air resistance
air resistance leads to smaller max. height and shorter range
time is trickier b/c air resistance decreases trip upward and increase trip downward
air resistance has greater effect on faster moving bodies .:. trip upward is decreased moreso than tripdownward is increase
"the trip is still shortened"

Also I don't understand #97
How are time t and angle ø (theta) related?
A. As ø increases, t increases
B. As ø increases, t decreases
C. As ø increases, t increases then decreases
D. As ø increases, t remains the same

ans was A

solutions manual said:
as ø increases, vertical velocity increases
time of flight is directly proportional to vertical velocity by v = gt/2

 

[Cawolf]

It looks like a standard projectile with a initial angle θ and velocity v.

-V, initial velocity, this will not be effected by anything as it is given and set at release, before drag interacts, so this must be the answer (C).

-H, height, is created by the upward velocity of the object ( vsin θ ). The drag force created will directly oppose this motion and decrease the height.

-R, Range with the same initial and final height is R = (v^2)(sin2 θ )/g. It is dependent on the square of the initial velocity and because the drag force in the opposite direction will oppose the objects horizontal travel - the range must decrease.

-The time will decrease for multiple reasons. Decrease in upward and forward velocity with time due to drag will shorten the distance the projectile travels. Though the upward velocity will slow (increasing time?), the downward velocity will be slowed even more due to the fact that drag is proportional to the square of the velocity - so overall there will be a decrease in time.

If you have trouble seeing it look at this graphic I found, the black path experiences no drag.



Source :
http://en.wikipedia.org/wiki/Drag_(physics)

Though in my opinion this question is looking to see if you understand that the initial velocity is not effected, and that should be your take home message as it will save you much time with questions like this.

 

[el_duderino]

Time in flight is determined by how high the projectile goes.

The projectile goes highest when aimed straight up.

This answers both questions.

 

[Cawolf]

Now for number 97 - this problem is looking to address how the initial angle θ effects the time of travel.

The max time will occur when h is the greatest. If we take the acceleration in the y direction and integrate to the y velocity, we know that the max height is achieved when the y velocity is zero, as the projectile is "changing" from rising to falling. Plugging in 0 for the velocity and solving for time gives us an equation that t = Vsinθ/g. The value is maximized at θ =90 which is vertically upwards. So therefore the correct answer is A - as we increase θ to be straight up the time will increase. This is when the initial vertical velocity is maximized.

 

[JMMTB]

As far as question 96 air resistance doesn't have any effect on the initial velocity (in ideal physics) just after it is fired. Air resistance creates drag thus decreasing the range, height, and flight time of a projectile.