Question pattern: Projectile with fluid resistance
Original question 1 of 2 in this pattern
Compare ideal and resisted projectile motion
Two launches have the same initial speed, direction and launch height. Model I neglects fluid resistance. Model R includes fluid resistance. The listed values are observations from the two resulting trajectories; no drag-force equation is supplied.
a) Compare the observed time of flight, maximum height and range.
b) Explain why the horizontal velocity in Model R decreases during flight.
c) Explain why the acceleration in Model R is not a constant vertically downward vector of magnitude g.
| Model | Time of flight / s | Maximum height / m | Range / m |
|---|---|---|---|
| I: resistance neglected | 3.2 | 12.5 | 44.0 |
| R: resistance included | 2.9 | 10.2 | 35.6 |
Worked answer
Solution
- Step 1
The observations show that Model R has a shorter flight time, a lower maximum height and a smaller range than Model I for this stated pair of trajectories.
- Step 2
In Model R, resistance has a component opposite the horizontal motion, so the horizontal velocity decreases rather than remaining constant.
- Step 3
The acceleration is the rate of change of the full velocity vector. Because the resistance contribution changes in magnitude and direction with velocity, the total acceleration is not constant and is not always vertically downward with magnitude g.
- Step 4
The resisted trajectory is therefore not the symmetric parabola produced by the ideal constant-acceleration model.
Final answer
For the supplied observations, resistance gives a shorter flight time, lower maximum height and smaller range; horizontal speed decreases, and acceleration varies because the resistance contribution opposes the changing velocity.
Common mistake
Applying a made-up quantitative drag equation when the question asks only for qualitative interpretation of supplied observations.
Concepts tested
- fluid resistance
- projectile trajectory
- time of flight
- range
- changing acceleration
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