Question

A ball of 500g is dropped from a height of 10m. There is an energy loss of 10J due to air resistance. Determine its velocity just before it hits the ground.​

Answer 1

Given:-

A ball of 500g is dropped from a height of 10m. There is an energy loss of 10J due to air resistance.

• Mass=500g
• height=10m
• Energy Loss=10J

To Find:-

A Ball Is Dropping from a Height of 10m

So,

$\sf \: potential \: energy = mgh$

$= > p.e = 500g \times 10m {s}^{ - 2} \times 10m$

$= > p.e = 0.5kg \times 10m {s}^{ - 2} \times 10m$

$= > p.e = 50kg {m}^{2} {s}^{ - 2}$

$= > p.e = 50j$

It is given That 10J of energy is loss due to air resistance.

So,

$\sf \: Energy \: Left = 50j - 10j$

$= > 40j$

When the ball reaches the ground, its potential energy becomes zero as it is entirely converted into its kinetic energy

$\sf \: k.e = p.e$

$\therefore \: k.e = 40j$

$\sf \: k.e = \frac{1}{2} m {v}^{2} = 40j$

$= > \frac{1}{2} m {v}^{2} = 40j$

$= > \frac{1}{2} \times .05kg \times {v}^{2} = 40j$

$= > {v}^{2} = \frac{2 \times 40}{0.5}$

$= > {v}^{2} = \frac{80}{0.5}$

$= > {v}^{2} = 160$

$= > v = \sqrt{160}$

$= > v = 12.64m {s}^{ - 1}$