Question
You observe a ball that moves (33.6pm 0.2)cm in (11.49pm 0.02)s . What is the observed speed of the ball (best estimate and most probable uncertainty)? (speed=distance/time) (1.62pm 0.01)cm/s (1.739pm 0.005)cm/s (2.92pm 0.01)cm/s (2.92pm 0.02)cm/s (1.619pm 0.008)cm/s
Answer
4.1
(167 Votes)
Ernest
Veteran · Tutor for 9 years
Answer
# Brief Explanations:To find the observed speed, we use the formula
. The best estimate is calculated by dividing the distance by the time. To find the uncertainty, we use the propagation of uncertainties formula for division: \( \frac{\Delta v}{v} = \sqrt{\left(\frac{\Delta d}{d}\right)^2 + \left(\frac{\Delta t}{t}\right)^2} \).# Answer:The observed speed is
.To find the uncertainty:
Thus, the uncertainty in speed is:
Rounding to match the significant figures:
Therefore, the observed speed is:
# Answer: