Explanation

We use the centripetal acceleration formula:

$$\mathrm{<b><font\; color="\#0000ff">a</font></b>}<b><font\; color="\#0000ff">=</font></b>\frac{{\mathrm{<b><font\; color="\#0000ff">v</font></b>}}^{\mathrm{<b><font\; color="\#0000ff">2</font></b>}}}{\mathrm{<b><font\; color="\#0000ff">r</font></b>}}$$

First, convert speed from km/h to m/s:

$$\mathrm{<b><font\; color="\#0000ff">90</font></b>}\text{<b><font color="\#0000ff"> km/h</font></b>}<b><font\; color="\#0000ff">=</font></b>\mathrm{<b><font\; color="\#0000ff">90</font></b>}<b><font\; color="\#0000ff">\times </font></b>\frac{\mathrm{<b><font\; color="\#0000ff">1000</font></b>}}{\mathrm{<b><font\; color="\#0000ff">3600</font></b>}}<b><font\; color="\#0000ff">=</font></b>\mathrm{<b><font\; color="\#0000ff">25</font></b>}\text{<b><font color="\#0000ff"> m/s</font></b>}$$

Now,

$$\mathrm{<b><font\; color="\#0000ff">a</font></b>}<b><font\; color="\#0000ff">=</font></b>\frac{<b><font\; color="\#0000ff">(</font></b>\mathrm{<b><font\; color="\#0000ff">25</font></b>}{<b><font\; color="\#0000ff">)</font></b>}^{\mathrm{<b><font\; color="\#0000ff">2</font></b>}}}{\mathrm{<b><font\; color="\#0000ff">100</font></b>}}<b><font\; color="\#0000ff">=</font></b>\frac{\mathrm{<b><font\; color="\#0000ff">625</font></b>}}{\mathrm{<b><font\; color="\#0000ff">100</font></b>}}<b><font\; color="\#0000ff">=</font></b>\mathrm{<b><font\; color="\#0000ff">6.25</font></b>}\text{<b><font color="\#0000ff"> </font></b>}{\text{<b><font color="\#0000ff">m/s</font></b>}}^{\mathrm{<b><font\; color="\#0000ff">2</font></b>}}$$

Explanation

In an isolated system with no external forces, the total momentum remains constant.

This principle is fundamental in collisions and rocket motion.

Explanation

We can solve this using the kinematic equation for motion under constant acceleration (gravity):

$${\mathrm{<b><font\; color="\#0000ff">v</font></b>}}^{\mathrm{<b><font\; color="\#0000ff">2</font></b>}}<b><font\; color="\#0000ff">=</font></b>{\mathrm{<b><font\; color="\#0000ff">u</font></b>}}^{\mathrm{<b><font\; color="\#0000ff">2</font></b>}}<b><font\; color="\#0000ff">+</font></b>\mathrm{<b><font\; color="\#0000ff">2</font></b>}\mathrm{<b><font\; color="\#0000ff">a</font></b>}\mathrm{<b><font\; color="\#0000ff">s</font></b>}$$

Where:

• $v=0$ m/s (at maximum height)

• $u=196$ m/s (initial velocity)

• $a=-9.8$ m/s² (acceleration due to gravity)

• $s=h$ (maximum height)

$$\mathrm{<b><font\; color="\#0000ff">0</font></b>}<b><font\; color="\#0000ff">=</font></b><b><font\; color="\#0000ff">(</font></b>\mathrm{<b><font\; color="\#0000ff">196</font></b>}{<b><font\; color="\#0000ff">)</font></b>}^{\mathrm{<b><font\; color="\#0000ff">2</font></b>}}<b><font\; color="\#0000ff">+</font></b>\mathrm{<b><font\; color="\#0000ff">2</font></b>}<b><font\; color="\#0000ff">(</font></b><b><font\; color="\#0000ff">-</font></b>\mathrm{<b><font\; color="\#0000ff">9.8</font></b>}<b><font\; color="\#0000ff">)</font></b>\mathrm{<b><font\; color="\#0000ff">h</font></b>}$$$$\mathrm{<b><font\; color="\#0000ff">0</font></b>}<b><font\; color="\#0000ff">=</font></b>\mathrm{<b><font\; color="\#0000ff">38416</font></b>}<b><font\; color="\#0000ff">-</font></b>\mathrm{<b><font\; color="\#0000ff">19.6</font></b>}\mathrm{<b><font\; color="\#0000ff">h</font></b>}$$$$\mathrm{<b><font\; color="\#0000ff">19.6</font></b>}\mathrm{<b><font\; color="\#0000ff">h</font></b>}<b><font\; color="\#0000ff">=</font></b>\mathrm{<b><font\; color="\#0000ff">38416</font></b>}$$$$\mathrm{<b><font\; color="\#0000ff">h</font></b>}<b><font\; color="\#0000ff">=</font></b>\frac{\mathrm{<b><font\; color="\#0000ff">38416</font></b>}}{\mathrm{<b><font\; color="\#0000ff">19.6</font></b>}}$$$$\mathrm{<b><font\; color="\#0000ff">h</font></b>}<b><font\; color="\#0000ff">=</font></b>\mathrm{<b><font\; color="\#0000ff">1960</font></b>}\text{<b><font color="\#0000ff"> meters</font></b>}$$

Explanation

A unit vector has a magnitude of 1 and points in the direction of a given vector.

It is used to represent direction only, without altering magnitude.

Explanation

Explanation

• The standard International System of Units (SI) unit for molar volume is cubic meters per mole
• Depending on the state of the substance, practical chemistry and physics work use alternate metric units, such as
•  m³/mol
• dm³/mol
• cm³/mol.

Additional information

mol/L:

This is the unit for molarity, which represents the concentration of a solution. 

g/mol:

This is the unit for molar mass, which is the mass of one mole of a substance. 

mol/g:

This is the inverse of molar mass, not a standard unit for molar volume. 

Explanation

To convert Celsius to Fahrenheit, multiply the Celsius temperature by 1.8 (or 9/5) and then add 32.

The exact formula is

°F = (°C × 9/5) + 32

Explanation

• Ideal gas equation: PV = nRT  
• To solve for n (moles):  
• n = PV / RT

Here is what each variable represents:=

n: Number of moles

P: Pressure of the gas

V: Volume of the gas

R: Ideal gas constant

T: Absolute temperature in Kelvin

Explanation

• According to Boyle's law, the pressure of the gas will double
• Boyle’s Law: P₁V₁ = P₂V₂ (Pressure × Volume = constant at constant temperature)
• If volume becomes V/2, then:  

P × V = P₂ × (V/2)  

⇒ P₂ = 2P  

Explanation

• Area is a derived quantity
• Because it is calculated by multiplying two base quantities together (Length × Width).
• A derived quantity is a physical property calculated by combining two or more base (fundamental) quantities through multiplication or division

Additional information

• Mass, Length, and time are all base quantities
• Which means they are fundamental physical quantities that cannot be defined in terms of other quantities.