# Solution to #1-3

Paper 2 Difficulty: Medium

A bullet travels a distance of $l=154\pm0.5$ m in the time $t=0.4\pm0.05$ s.

a) Calculate the fractional uncertainty for the speed of the bullet.

[Maximum mark: 2]

$\frac{\Delta v}{v}=\frac{\Delta l}{l}+\frac{\Delta t}{t} \\ \frac{\Delta v}{v}=\frac{0.5}{154}+\frac{0.05}{0.4}\\ \frac{\Delta v}{v}=0.12825\approx0.13$

b) Calculate the percentage uncertainty for the speed of the bullet.

[Maximum mark: 1]

$0.13\times100=13\%$

c) Write down the speed of the bullet using the absolute uncertainty.

[Maximum mark: 2]

$v=\frac{154}{0.4}=385\ \textrm {ms}^{-1}\\ \frac{\Delta v}{v}=0.13\\ \Delta v=385\times 0.13=50\ \textrm {ms}^{-1} \\ v=385\pm 50\ \textrm {ms}^{-1}$