## Physics for Scientists and Engineers 3E by R. Knight, P1.23

#### d) 72 µm/ms

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## Solution:

The uncertainty is computed as

$\displaystyle \delta _m=\frac{3\:\%}{100\:\%}\times 65\:kg=1.95\:kg$           ☚

Therefore, the uncertainty in the given mass is 1.95 kg.

## College Physics Problem 1.10

#### b) What is this is meters per second?

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## Solution:

### Part a

We know that the formula for the distance traveled, d, if we are given rate, r, and time, t is given by $\displaystyle d=r\times t$

Therefore, the distance traveled is

$\displaystyle d=\left(4\:\frac{cm}{year}\times \frac{1\:year}{365\:\frac{1}{4}\:days}\times \frac{1\:day}{24\:hours}\times \frac{1\:hour}{60\:mins}\times \frac{1\:min}{60\:s}\right)\left(1\:s\right)$

$\displaystyle d=1.3\times 10^{-7}\:cm\:$

$\displaystyle d=1.3\times 10^{-9}\:m$

Therefore, the distance traveled by the tectonic plate is about $\displaystyle 1.3\times 10^{-9}\:m$          ☚

### Part b

We need to convert 4.0 cm/year to km/My.

$\displaystyle 4.0\:\frac{cm}{year}\times \frac{1\:m}{100\:cm}\times \frac{1\:km}{1000\:m}\times \frac{1\:000\:000\:years}{1\:My}=40\:\frac{km}{My}$

Therefore, the speed of the tectonic plates is 40 km/My.          ☚

## Solution:

We know that 1 km=1000 m and 1 hr=3600 sec.

Convert 342 m/s.

$\displaystyle 342\:m/s=\left(342\:\frac{m}{s}\right)\left(\frac{1\:km}{1000\:m}\right)\left(\frac{3600\:s}{1\:hr}\right)=1231.2\:km/hr$          ☚

Therefore, the speed of sound in km/hr is 1231.2 km/hr.

## Solution:

Convert 29028 ft to km

$\displaystyle 29,028\:ft=\left(29\:028\:ft\right)\left(\frac{1\:km}{3281\:ft}\right)=8.847\:km$          ☚

Therefore, the height of Mount Everest is 8.847 kilometers.

## Solution:

First, convert 6 ft to inches

$\displaystyle 6\:ft=\left(6\:ft\right)\left(\frac{12\:in}{1\:ft}\right)=72\:in$

$\displaystyle 72\:in\:+1\:in=73\:inches$
$\displaystyle 73\:in=\left(73\:in\right)\left(\frac{1\:m}{39.37\:in}\right)=1.85\:m$