Question

An elevator descends from a height of 10 m from above the ground. If it descends at a rate of $6\operatorname{m} /\min $ then what will be the time required for the elevator to reach a depth of -350 m?
Option A: 40 min.
Option B: 50 min.
Option C: 60 min.
Option D: 70 min.

Answer 1

Hint:the elevator has no acceleration so the velocity of the elevator will not change and so the final velocity will be equal to initial velocity. The net acceleration of the elevator is zero.

Complete solution:
If we understand the case, we will see that the total distance the elevator travels is 360 meters.
For better understanding let us have a look over the diagram given below;

The diagram above will help you get a better understanding of the situation given.
Now we all know that distance is the product of speed and time;
Mathematically we can write;
$s = ut$ (Here, u = speed of the body, t = time taken and s= distance covered)
So,
$s = 360m = ut$
Also,
$u = 6m/\min $
$ \Rightarrow u = \dfrac{6}{{60}}m{s^{ - 1}}$
$ \Rightarrow u = 0.1m{s^{ - 1}}$
Thus we substitute these values in the formula;
$s = ut$
$ \Rightarrow 360 = 0.1t$
$ \Rightarrow t = \dfrac{{360}}{{0.1}}\sec $
$ \Rightarrow t = 3600\operatorname{s} $
$\therefore t = 1hr = 60\min $

Hence option C is correct.

Note:
-The fact that the acceleration is zero is due to the elevator rope.
-The only force acting on the elevator downwards is the gravitational pulling force, and this force is balanced by the upward pulling tension force due to the rope.
-So the acceleration due to gravity is cancelled by the deceleration of the tension force due to the rope.
-Hence the elevator moves with a steady velocity.