Question

A paper weight is dropped from the roof of a block of multistorey flats, each storey being 3 meters high. It passes the ceiling of the 20th storey at 30 m/s. If $g = 10m/{s^2}$, how many storeys does the flat have?
A. 25
B. 30
C. 35
D. 40

Answer 1

Hint: The height of each storey, the final velocity and the number of the storey it stopped are given. So use the third equation of motion to find the distance travelled by paper by substituting the values of initial velocity which is zero, final velocity and acceleration due to gravity. We get the distance travelled by the paper. Divide it by 3 to get the no. of storeys it travelled. Add this number to 20 to get the total number of storeys that the flat has.

Formula Used: Third equation of motion is ${v^2} = {u^2} + 2as$, where u is the initial velocity, v is the final velocity, s is the distance travelled and a is the acceleration.

Complete step by step answer:We are given that each storey of a flat is 3 m high and a paper is dropped from the roof and stopped at 20th storey with velocity 30m/s. We have to find the no. of storeys flat has.
As the paper is moving downwards, acceleration acting on the paper is acceleration due to gravity and the initial velocity of the paper is 0.
Therefore, distance travelled by the paper from the roof is
$
  {v^2} = {u^2} + 2as \\
  u = 0,v = 30,a = 10 \\
   \Rightarrow {30^2} = {0^2} + 2 \times 10 \times s \\
   \Rightarrow 20s = 900 \\
   \Rightarrow s = \dfrac{{900}}{{20}} \\
  \therefore s = 45m \\
 $
Therefore, the distance travelled by the paper weight is 45m.
The height of each storey is 3m.
No. of storeys it travelled is $\dfrac{{45}}{3} = 15$
The paper weight stopped at the 20th storey from the bottom and it already travelled 15 storeys from the roof.
Therefore, the total no. of storeys of the flat are $20 + 15 = 35$
The correct option is Option C.

Note:Acceleration is the rate of change of velocity of a body and acceleration produced by gravity is called acceleration due to gravity (g). Acceleration due to gravity is constant for every creature on the earth whereas normal acceleration changes with the velocity. So be careful with these two terms.