Density = (mass) divided by (volume)
We know the mass (2.5 g). We need to find the volume.
The penny is a very short cylinder.
The volume of a cylinder is (π · radius² · height).
The penny's radius is 1/2 of its diameter = 9.775 mm.
The 'height' of the cylinder is the penny's thickness = 1.55 mm.
Volume = (π) (9.775 mm)² (1.55 mm)
= (π) (95.55 mm²) (1.55 mm)
= (π) (148.1 mm³)
= 465.3 mm³
We know the volume now. So we could state the density of the penny,
but nobody will understand what we have. Here it is:
mass/volume = 2.5 g / 465.3 mm³ = 0.0054 g/mm³ .
Nobody every talks about density in units of ' gram/(millimeter)³ ' .
It's always ' gram / (centimeter)³ '.
So we have to convert our number for the volume.
(0.0054 g/mm³) x (10 mm / cm)³
= (0.0054 x 1,000) g/cm³
= 5.37 g/cm³ .
This isn't actually very close to what the US mint says for the density
of a penny, but it's in a much better ball park than 0.0054 was.
<h2><u>We have</u>,</h2>
- Initial velocity (u) = 0 m/s
- Time taken (t) = 2.9s
- Acceleration due to gravity (g) = + 10 m/s² [Down]
<h2><u>To calculate</u>,</h2>
- Final velocity (v)
- Height (h)
<h2><u>Solution</u><u>,</u></h2>
→ v = u + gt
→ v = 0 + 10(2.9)
→ v = 29 m/s 
… ( Ans )
And,
→ h = ut + ½gt²
→ h = 0(2.9) + ½ × 10 × (2.9)²
→ h = 5 × 8.41
→ h = 42.05 m … ( Ans )
Explanation:
Given
initial speed(u)=3 m/s
mass of each ball is m
Let the cue ball is moving in x direction initially
In elastic collision Energy and momentum is conserved
Let u be the initial velocity and 
be the final velocity of 8 ball and cue ball respectively
The angle after which cue ball is deflected is given by
Conserving momentum in x direction
Along Y axis
substitute the value of 
we get 
The measure of the force of gravity on an object, expressed as mass of the object times acceleration due to gravity is called
weight
