Question

please answer the above numerical with step by step explanation​

Answer 1

In order to solve this question u need to understand the topic of relative motion

As the entire motion of the elevator takes place in vertical direction ,let us consider upward direction as positive and downward direction as negative

We need to find the time taken by the coin to reach the floor in order to do this we need to use the second kinematic equation of motion

The acceleration and velocity of of the elevator and coin is given  wrt to ground .First we need to find the acceleration and velocity of of the elevator and coin  wrt to elevator

As per the given question ,

acceleration of elevator wrt ground = +2 m/s (as elevator is moving in upward direction

acceleration of coin wrt ground = - 10 m/s^2

according to the concept of relative motion ,

$\rightarrow\mathtt{a_{ce}=a_{cg} - a_{eg}}$

$\rightarrow\mathtt{a_{ce}= - 10 - (+2)}$

$\rightarrow\mathtt{a_{ce}= - 12 \dfrac{m}{s^{2} }}$

initially velocity of elevator wrt ground = +10 m/s

initially velocity of coin wrt ground = + 10 m/s

(as initially both the system are moving together in upward direction )

$\rightarrow\mathtt{u_{ce}=u_{cg} - u_{eg}}$

$\rightarrow\mathtt{u_{ce}=10 - 10}$

$\rightarrow\mathtt{u_{ce}=0}$

distance traveled by the coin = - 1.5 m ( as the coin is moving in downward direction )

By using the second equation of motion ,

$\rightarrow\mathtt{s = ut + \dfrac{1}{2}at^{2} }$

$\rightarrow\mathtt{- 1.5 = 0 \times t + \dfrac{1}{2}\times (-12)t^{2} }$

$\rightarrow\mathtt{- 1.5 = - 6t^{2} }$

$\rightarrow\mathtt{t^{2} = \dfrac{1.5}{6} }$

$\rightarrow\mathtt{t^{2} = \dfrac{15}{60} }$

$\rightarrow\mathtt{t^{2} = \dfrac{1}{4}}$

$\rightarrow\mathtt{t = \dfrac{1}{2}sec}$

The time taken by the coin to reach the floor is 1/2 sec