Question: A ball is dropped from the top of a building. The ball takes 0.5 s to fall past the window 3 m in le...

Question

A ball is dropped from the top of a building. The ball takes 0.5 s to fall past the window 3 m in length at a certain distance from the top of the building. (g= $10m{s^{ - 2}}$ )
Speed of the ball as it crosses the top edge of the window is
${\text{A}}{\text{. }}3.5m{s^{ - 1}} \\\ {\text{B}}{\text{. }}8.5m{s^{ - 1}} \\\ {\text{C}}{\text{. }}5m{s^{ - 1}} \\\ {\text{D}}{\text{. }}12m{s^{ - 1}} \\\$

Answer 1

Solution

Here we go through by writing the given terms in the question with their respective sign convention. Then we apply the formula of kinematics to find the terms which the question asked.

Complete answer:
Here in the question it is given that a ball is dropped from the top of a building. The ball takes 0.5 s to fall past the window 3 m in length at a certain distance from the top of the building.
It means that the distance travelled by the ball from top edge of window to lower edge of the window is 3m.
I.e. s=3m
And the time taken by it to travel such a distance is given by 0.5s.
I.e. t=0.5s.
And the acceleration due to gravity is given i.e. a= $10m{s^{ - 2}}$
And we have to find out the initial velocity of the ball when it starts traveling through the window.
As we know that the formula of kinematic when the distance travelled, acceleration and time is given we apply the formula $s = ut + \dfrac{1}{2}a{t^2}$ to find out the initial velocity.
Now put the following data in the formula we get,
Taking downward direction as positive.
s=3m
a= $10m{s^{ - 2}}$
t=0.5s
$\Rightarrow 3 = u(0.5) + \dfrac{1}{2} \times 10 \times {(0.5)^2} \\\ \Rightarrow 3 - 1.25 = u(0.5) \\\ \Rightarrow u = \dfrac{{1.75}}{{0.5}} = 3.5m{s^{ - 1}} \\\$
Therefore the speed of the ball as it crosses the top edge of the window is $3.5m{s^{ - 1}}$ .

So, the correct answer is “Option A”.

Note:
Whenever we face such a type of question the key concept for solving the question is to first of all find the formula in which all the terms are satisfying and the one term is missing so that we find out the unknown term from that formula that is the answer of our question.