Question

a object of mass 1kg is thrown vertically upward with a velocity of 60 m/s the ratio of kinetic energy to its potential energy after 8 seconds is

Answer 1

The ratio of kinetic energy to its potential energy after 8 seconds is 9:40

Given : An object object of mass 1kg is thrown vertically upward with a velocity of 60 m/s.

To find : The ratio of kinetic energy to its potential energy after 8 seconds.

Solution :

We can simply solve this numerical problem by using the following process. (our goal is to calculate the ratio of kinetic energy to its potential energy after 8 seconds)

First of all, we have to calculate the height of the object after 8 seconds.

For calculating height of the object, we will be using the following mathematical formula.

s = ut + ½ at²

Here,

• s = displacement
• u = initial velocity
• a = acceleration
• t = time

In the given case,

• s = height of the object = unknown
• u = initial velocity = 60 m/s
• a = gravitational acceleration = 10 m/s²
• t = 8 seconds

So,

The height of the object will be :

= (60 × 8) + (½ × 10 × 8²)

= 480 + 320

= 800 m

Now,

Potential energy = mass × gravitational acceleration × height

Here, mass = 1 kg = 1000g

So,

Potential energy of the object = 1000 × 10 × 800 = 8000000 J

And,

Kinetic energy = ½ × mass × (velocity)²

So,

Kinetic energy of the object = ½ × 1000 × (60)² = 1800000 J

Now,

The ratio will be :

= 1800000 : 8000000

= 18 : 80

= 9 : 40

(This will be considered as the final result.)

Hence, the ratio of kinetic energy to potential energy will be 9 : 40