Question

A body falls from the top of a building and reaches
the ground 2.5 s later. How high is the building ?
(Take g = 9.8 m s-2)
Ans. 30.6 m.
As you know answer is given you should explain it​

Answer 1

Given : -

A body falls from the top of a building and reaches the ground after 2.5 seconds .

Required to find : -

• Height of the building ?

Equations used : -

❶ v = u + at

❷ v² - u² = 2as

Here,

• v = Final velocity

• u = Initial velocity

• a = acceleration

• t = time taken

• s = displacement

Solution : -

A body falls from the top of a building and reaches the ground after 2.5 seconds .

we need to find the height of the building .

From the given data we can conclude that ;

• Initial velocity of the body ( u ) = 0 m/s

• Time taken ( t ) = 2.5 seconds

Since , it is falling freely . And we know that when a body falls freely acceleration due to gravity acts on it .

So,

• Acceleration due to gravity ( g ) = 9.8 m/s²

Now,

Let's find the final velocity ;

Using the Equation of motion ,

i.e v = u + at

➛ v = 0 + 9.8 x 2.5

➛ v = 9.8 x 2.5

➛ v = 24.5 m/s²

Hence,

• Final velocity of the body ( v ) = 24.5 m/s²

Now,

Let's find the displacement of the body !

Using the equation of motion ;

i.e. v² - u² = 2as

➛ ( 24.5 )² - ( 0 )² = 2 x 9.8 x s

➛ 600.25 - 0 = 2 x 9.8 x s

➛ 600.25 = 2 x 9.8 x s

➛ 600.25 = 19.6 x s

➛ 600.25 = 19.6s

➛ 19.6s = 600.25

➛ s = 600.25/19.6

➛ s = 60025/1960

➛ s = 30.625

➛ s = 30.6 meters ( approx. )

Hence,

• Displacement of the body ( s ) = 30.6 meters ( approx. )

Here,

We need to apply a bit of logic ;

The logic is the displacement of the body is equal to height of the building .

Therefore,

• Height of the building = 30.6 meters ☜