Question

In physics lab, you measure three quantities: x , y , and z . Suppose that x = 1.1 cm , y = 0.8 s , and z = 3.9 cm/s . Which of the mathematical combinations might be meaningful?

Answer 1

Answer:

a) $xyz$

b) $\frac{x}{z}-y$

e) $\frac{xy}{z}$

h) $x-\frac{y}{z}$

Explanation:

The given options are:

a) $xyz$

b) $\frac{x}{z}-y$

c) $\frac{x-y}{z}$

d) $xz+y$

e) $\frac{xy}{z}$

f) $x+y+z$

g) $\frac{x}{y}-z$

h) $x-\frac{y}{z}$

Let's try with each of them and find the mathematical combinations that might be meaningful, taking into account $x=1.1 cm$, $y=0.8 s$  and $z=3.9 cm/s$. This means we have to be careful with the units:

a) $xyz$

Here we have a mulitplication:

$(1.1. cm)(0.8 s)(3.9 cm/s)=3.43 cm^{2}$ Could be meaningful

b) $\frac{x}{z}-y$

$\frac{1.1 cm}{3.9 cm/s}-0.8 s=0.28 s - 08 s=-0.51 s$ Could be meaningful

c) $\frac{x-y}{z}$

$\frac{1.1 cm-0.8 s}{3.9 cm/s}$ Not meaningful, since we cannot operate summing and subtracting with two different units.

d) $xz+y$

$(1.1 cm)(3.9 cm/s)+0.8 s=4.29 cm^{2}/s+0.8 s$ Not meaningful, since we cannot operate summing and subtracting with two different units.

e) $\frac{xy}{z}$

$\frac{(1.1 cm)(0.8 s)}{3.9 cm/s}=0.22 s^{2}$ Could be meaningful

f) $x+y+z$

$1.1 cm+0.8 s+3.9 cm/s$ Not meaningful, since we cannot operate summing and subtracting with different units.

g) $\frac{x}{y}-z$

$\frac{1.1 cm}{0.8 s}-3.9 cm/s$ Not meaningful, since we cannot operate summing and subtracting with different units.

h) $x-\frac{y}{z}$

$1.1 cm-\frac{0.8 s}{3.9 cm/s}=0.89 cm$ Could be meaningful