Question

A stone is dropped from a 25thstorey of multistorybuilding and it reaches the ground in 5s. In the first second it passes
through how stories of the building?​

Answer 1

Answer:

Let the height of each storey =h

2

nd

equation of motion from starting point to A-

h

1

=0+

2

1

g(1)

2

⇒h

1

=

2

g

2

nd

equation of motion from starting point to B-

25h=0+

2

1

×g×(25)

25h=

2

25g

⇒h=

2

g

h=h

1

In one second it passes one storey

Answer 2

Answer:

Number of storey the stone passes through = 1

Explanation:

$\Large{\underline{\rm{Given:}}}$

• The stone is thrown from the top of a 25 storey building.
• The stone reaches the ground in 5 seconds
• Initial velocity = 0 m/s

$\Large{\underline{\rm{To\:Find:}}}$

• Number of storeys the stone passes through in the first second

$\Large{\underline{\rm{Solution:}}}$

Here let us assume that the height of each storey of the building is s m.

Given that there are 25 stories in the building.

Hence the total distance travelled by the stone = 25s m

By the second equation of motion we know that,

s = ut + 1/2 × a × t²

where s = distance travelled

u = initial velocity

a = g = acceleration due to gravity = 9.8 m/s²

t = time taken

Substitute the data,

25s = 0 × 5 + 1/2 × 9.8 × 5²

25s = 122.5

s = 122.5/25

s = 4.9 m

Hence the height of each storey of the building is 4.9 m.

Now let the stone pass through x number of stories in its first second.

Hence,

s = ut + 1/2 × a × t²

Here time taken = 1s, distance travelled = 4.9 x m

Therefore,

4.9 x = 0 × 1 + 1/2 × 9.8 × 1²

4.9 x = 4.9

x = 4.9/4.9

x = 1

Hence the stone passes through one storey of the building in its first second.