Simple question on Kinematics:
A photographer wishes to check the time for which the shutter on a camera stays open when a photograph is being taken. To do this, a metal ball is photographed as it falls from rest. It is found that before the shutter opens, the balls falls 2.50 m from rest and, during the time that the shutter remains open, the ball falls a further 0.12 m, as illustrated in the figure on the right. Assuming that air resistance is negligible, calculate
(i) the speed of the ball after falling 2.50m,
(ii) the time to fall the further 0.12m.
The time for which the shutter stays open is marked on the camera as 1/160 s. Comment on whether the test confirms this time.
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Answer:
(i) Using v² = u² + 2as,
v² = 0 + 2(9.81)(2.50)
v = 7.00 ms-1
(ii) Using s = ut + ½at²,
0.12 = 7t + ½(9.81)t²
=> 0.7t² + t - 0.01713 = 0
t = 0.0169 s
Shutter speed = 1/60 = 0.0167 s
Thus, fractional error = (0.0167 - 0.0165) / 0.0167 = 0.01 (very small)
Thus, the given shutter speed is confirmed by the test.
