Question

How long does a ball take to fall from a roof to the ground $ 7m $ below?

Answer 1

Hint: We should know that velocity is defined as the rate change of displacement per unit time. Speed in a specific direction is also called the velocity. Here in this question a ball is dropped from a roof to the ground. We should know the formula of distance travelled i.e. $ s = ut + \left( {\dfrac{1}{2}} \right)a{t^2} $ , where $ s $ is the distance travelled.

Complete step by step solution:
Let us assume that there is no air resistance and the only force acting on the ball is the gravity, so we can use the equation of motion: $ s = ut + \left( {\dfrac{1}{2}} \right)a{t^2} $ .
Here $ s $ is the distance travelled, $ u = $ initial velocity which is zero, $ t = $ time to travel given distance and $ a = $ acceleration. But in this case $ a = g $ , the acceleration of free fall which is $ 9.81m{s^{ - 2}} $ .
Hence by substituting the values in the formula, we have:
 $ 7 = 0t + \left( {\dfrac{1}{2}} \right)9.81{t^2} $ .
We will now solve it: $ 7 = 0 + 4.905{t^2} \Rightarrow {t^2} = \dfrac{7}{{4.905}} $ .
It gives us the value $ t \approx 1.195s $ .
Hence it takes barely a second for the ball to hit the ground from that height.
So, the correct answer is “$ t \approx 1.195s $”.

Note: We should know that velocity is a vector quantity i.e. it is direction aware. An object which moves in the negative direction has a negative velocity. Also we should note that if an object’s speed or velocity is increasing at a constant rate then we can say it has an uniform acceleration. The rate of acceleration is constant.