SI UNITS - EXAMPLES II

11. Determine how much water can be in cuboid with dimensions of 2 m x 1 m x 0.5 m? If the water density is equal to 1 g/cm³ determine how much kilograms of water can be inside the cuboid?

$$\begin{align} & a=2\text{ m} \\ & b=1\text{ m} \\ & \underline{\begin{align} & c=0.5\text{ m} \\ & \rho \text{=1g/c}{{\text{m}}^{3}} \\ \end{align}} \\ & V=? \\ & m=? \\ & \rho =1\left[ \frac{\text{g}}{\text{c}{{\text{m}}^{3}}} \right]\frac{1\text{ }\left[ \text{kg} \right]}{1000\text{ }\left[ \text{g} \right]}\frac{1000000\text{ }\left[ \text{c}{{\text{m}}^{3}} \right]}{1}=1000\text{ kg/}{{\text{m}}^{3}} \\ & V=abc=2\cdot 1\cdot 0.5=1\text{ }{{\text{m}}^{3}} \\ & m=\rho V=1000\cdot 1=1000kg \\ \end{align}$$

12. How much seconds has one day?

$$\begin{align} & \underline{n=1\text{ day}=24\text{ h}} \\ & n=?s \\ & 1\text{ h}=60\text{ min} \\ & n=24\left[ \text{h} \right]\cdot \frac{60\text{ }\left[ \min \right]}{1\text{ }\left[ \text{h} \right]}=1440\text{ }\min \\ & 1\text{ min}=60\text{ s} \\ & n=1440\text{ }\left[ \min \right]\cdot \frac{60\text{ }\left[ \text{s} \right]}{1\text{ }\left[ \min \right]}=86400\text{ s} \\ \end{align}$$

13. What is the height of an equilateral triangle with side length of 10 cm?

$$\begin{align} & \underline{a=10\text{ cm}=0.1\text{ m}} \\ & \text{h=?} \\ & h=\frac{\sqrt{3}}{2}a=\frac{\sqrt{3}}{2}\cdot 0.1=0.0866025\text{ m} \\ \end{align}$$

14.The height of an equilateral triangle is 5 cm. Determine the side length?

$$\begin{align} & \underline{h=5\text{ cm}=0.05\text{ m}} \\ & a=? \\ & h=\frac{\sqrt{3}}{2}a \\ & a=\frac{2h}{\sqrt{3}}=\frac{2\cdot 0.05}{\sqrt{3}}=0.0577\text{ m} \\ \end{align}$$

15. Rectangular triangle with cathetus of length 3 cm and 4 cm. What is the length of the hypotenuse?

$$\begin{align} & a=3\text{ cm}=0.03\text{ m} \\ & \underline{b=4\text{ cm}=0.04\text{ m}} \\ & c=? \\ & c=\sqrt{{{a}^{2}}+{{b}^{2}}}=\sqrt{{{0.03}^{2}}+{{0.04}^{2}}}=0.05\text{ m} \\ \end{align}$$

16.Dependence of position of the body which is moving along x axis on time t is shown in the next figure.

Determine:

a.       Where was the body at the moment: t₁ = 1 s, t₂ = 3 s, t₃ = 5 s, t₅ = 8 s

b.      In which time interval is the body at rest?

c.       In what intervals the body has positive shift and in what has a negative shift?

$$\begin{align} & {{t}_{1}}=1\text{ s} \\ & {{t}_{2}}=3\text{ s} \\ & {{t}_{3}}=5\text{ s} \\ & \underline{{{t}_{4}}=8\text{ s}} \\ & a){{s}_{1}}=40\text{ m}\text{, }{{s}_{2}}=80\text{ m}\text{, }{{s}_{3}}=80\text{ m}\text{, }{{s}_{4}}=20\text{ m} \\ & \text{b)t}\in \left[ 2,6 \right] \\ & c)\text{ Positive shift in time interval t}\in \left[ 0,2 \right] \\ & \text{Negative shift in time interval t}\in \left[ 6,10 \right] \\ \end{align}$$