Question

A swimmer covers the 50-yard freestyle in a time of 0:2805 (28.05 sec), measured by electronic timer pads The double length of the pool measures as s . 50.0 ± 0.5 yards. The time can be taken as t 28.05 ±0.01 sec. The resulting speed, according to ves/t, Is then 1.78 yards/s Which of the following would be an acceptable way to give the uncertainty of the speed v? 0 Δu=0.5prd/s since the distance has the larger uncertainty. 。Aw = 0.5ー+ 50. Ord x 0.018 = 0.021/rd/8 28.05 (28.05 O Aw = 0.5yrd + 0.01 s = 0.51 yrd/s

Answer 1

then proportional error in speed v is given by

v = s/t then proportional error in speed v is given by delta v/v = delta s/s + delta t/t hence uncertainty in speed is given by delta v = (delta s/s + delta t/t) v Second option is more accurate way.

$\frac{\Delta v }{v}=\frac{\Delta s}{s}+\frac{\Delta t}{t}$

hence uncertainty in speed is given by

$\Delta v =\left ( \frac{\Delta s}{s}+\frac{\Delta t}{t} \right )v$

Second option is more accurate way.

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