Question

a ball of mass 2kg is thrown up with a speed of 10m/s. find the kinetic energy of the ball at the time of throwing. also find the potential energy of the ball at the highest point?

Answer 1

${\huge{\boxed{\mathcal{\red{Answer}}}}}$

Kinetic energy of object is the energy due to its motion. It is measured in joules.

Kinetic energy is also the half of product of mass and square of velocity of object.

Mathematically it is represented by :

$\frac{1}{2} \times m {v}^{2}$

Potential energy is the energy of an object due to its position. It is measured In joules.

Potential energy is also the product of mass, acceleration and displacement or height of an object.

Mathematically it is represented by :

$m \times g \times h$

______________________________________

It is given that :

Mass of object = 2kg

Initial velocity = 10m/s

Kinetic energy = ?

Potential energy = ?

____________________

Now, kinetic energy of this object will be :

$\frac{1}{2} \times m {v}^{2}$

$= \frac{1}{2} \times 2 \times {10}^{2}$

$= {10}^{2}$

$= 100j$

Thus kinetic energy of object is 100J.

Now for a body with some velocity when it reaches its maximum height the velocity of body becomes 0.

Thus final velocity of this object at Maximum height will be 0.

And according to third equation of motion :

${v}^{2} = {u}^{2} + 2as$

The height or displacement of this body is :

$s = \frac{ {v}^{2} - {u}^{2} }{2a}$

$s \: = \frac{ {0}^{2} - {10}^{2} }{2 \times - 9.8}$

$= \frac{ - 100}{ - 19.6}$

Here (-) before g represent vertical direction

$s = 5$

Thus maximum height reached by object is 5m.

Now the potential energy of object will be :

$2 \times 9.8 \times 5$

$= 98j$

______________________________________

BY√\______________ SCIVIBHANSHU

THANK YOU

STAY CURIOUS

Answer 2

We have,

Mass of particle = 2 kg

Intitial velocity = 10 m/s

Final velocity = 0 m/s

Acceleration due to gravity = - 10 m/s² {Up}

Kinetic energy = ½mv²

⇒K.E. = ½ × 2 kg × (10 m/s)²

⇒K.E. = 100 J ...(1)

Potential energy = mgh

Finding "h":-

Now we know, v² - u² = ± 2gh

⇒- u² = - 2gh

⇒u² = 2gh ⇒h = u²/2g

⇒h = (10 m/s)² ÷ [2 × 10 m/s²]

{taking g = 10 m/s²}

⇒h = (100 m²/s²)/[20 m/s²]

⇒h = 5 m

∴ P.E. = (2 kg)(10 m/s²)(5 m)

⇒P.E. = 100 Nm = 100 J ...(2)