14
votes
Apple falling from boat mast
You are not wrong of course. The examples are supposed to be idealized examples where we ignore air friction.
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13
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Effect of drag on projectile flight time - simple solution?
I don't think this can be easily proven - I think it depends on the viscosity of air and the speed with which the projectile is fired.
Under ordinary circumstances, I'm sure the main factor is that ...
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12
votes
Effect of drag on projectile flight time - simple solution?
The thick red line corresponds to the velocity of the ball without air resistance. Its gradient is $-g$.
It should be clear that with air resistance, you decelerate faster. Therefore you end up with ...
- 22.1k
10
votes
Effect of drag on projectile flight time - simple solution?
Two identical balls, x and y, are thrown up from the earth's surface with the same velocity. x is thrown in the air and y is in a vacuum. Which ball reaches a higher maximum height and which ball will ...
- 23.3k
9
votes
Effect of drag on projectile flight time - simple solution?
There is no simple intuitive explanation, because it's not true!
As explained in this paper, the answer depends on the model of air drag. If the drag force is proportional to $v^n$, it turns out the ...
- 105k
6
votes
Accepted
Ballistic curve in 3D space with launch offsets
It is indeed useful here to shift the coordinate system origin's to $\vec{P}$, via a simple translation, mainly so that the equations look a bit nicer. So everywhere in this post I assume $\vec{P}=(0,...
- 3,238
5
votes
Effect of drag on projectile flight time - simple solution?
I don't think one can prove "that drag causes a net increase in time" without some additional assumptions.
Let us consider the following example. Let us choose the initial speed of both ...
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3
votes
Effect of drag on projectile flight time - simple solution?
TL;DR: In this answer we consider an analytic approach beyond infinitesimal drag. OP's competition between damped fall vs. free fall turns out to be rather subtle.
Consider the 1D vertical damped ...
- 213k
2
votes
Effect of drag on projectile flight time - simple solution?
Continuing on @hft's answer, let's try to solve
$$
0 = -gt - (\alpha v_0 + g)\frac{1}{\alpha}\left(e^{-\alpha t} - 1\right)\;.
$$
In the Taylor series of that answer, we see terms of the form $v_0/g$ ...
2
votes
Effect of drag on projectile flight time - simple solution?
I'll start with the aside that the question neglects buoyancy; if the
"ball" is a party balloon, it could remain aloft for a long time, or
indefinitely if it is lighter than air.
Buoyancy ...
- 564
1
vote
Ballistic curve in 3D space with launch offsets
To solve your problem , you need 6 equations for the 3 components of the vector $~\vec d~$ , the 3 components of the vector $~\vec b~$, and 1 equation for the target time $~t_T~$, together 7 scalar ...
- 12.8k
1
vote
Accepted
Equations of motion in Earth-centered, Earth-fixed coordinates
Based on the corrections in the comments I believe the corrected force equation is:
$$ \underbrace{\dot{m} \mathbf{v}_{P/R}}_{\text{thrust}} - \underbrace{\frac{GMm}{r^2} \hat{\mathbf{r}}}_{\text{...
- 268
1
vote
What would the unit for the slope of a graph where the $x$-axis is mass and the $y$-axis is the drag coefficient?
By definition, the slope of a graph is the ratio between the vertical variation (drag coefficient) and the horizontal variation (mass). If you want the unit for the slope, it will therefore be $\text{...
- 58
1
vote
Accepted
How do you calculate the angular velocity vector only having access to the spin rate and the spin axis of a golf ball?
Spin rate (scalar $\dot{\theta}$) and spin axis (unit vector $\hat{u}$) combine to give the rotational velocity vector
$$ \vec{\omega} = \dot{\theta}\; \hat{u}$$
- 39.3k
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