Answer: 23000 frames/s
Explanation:
We know the maximum initial speed at which the seeds are dispersed is:
[tex]V_{i}=4,7 m/s[/tex]
In addition, we know the maximum distance at which the seeds move between photographic frames is:
[tex]d_{max}=0.20 mm \frac{1m}{1000 m}=0.0002 m[/tex]
And we need to find the minimum frame rate of the camera with these given conditions. This can be found by finding the time [tex]t[/tex] for each frame and then the frame rate:
Finding the time:
[tex]t=\frac{d_{max}}{V_{i}}[/tex]
[tex]t=\frac{0.0002 m}{4.6 m/s}[/tex]
[tex]t=0.00004347 s/frame[/tex] This is the time for each frame
Now we need to find the frame rate, which is the frequency at which the photos are taken.
In this sense, frequency [tex]f[/tex] is defined as:
[tex]f=\frac{1}{t}[/tex]
[tex]f=\frac{1}{0.00004347 s/frame}[/tex]
Finally:
[tex]f=23000 frames/s[/tex]
Hence, the minimum frame rate is 23000 frames per second.