Question

A body is projected vertically upward with an initial velocity u. If acceleration due to gravity is g, the time for which it remains in air, is
(A). $\dfrac{u}{g}$
(B). $ug$
(C). $\dfrac{{2u}}{g}$
(D). $\dfrac{u}{{2g}}$

Answer 1

Hint: Before approaching this question one must have prior knowledge of acceleration gravity, and remember to use the first equation of motion to find the value of the time, use these instructions to solve the given problem.

Complete step-by-step answer:
According to the question a body is projected (thrown) vertically upward. The velocity from which it was thrown is said as initial velocity and it is given u. We have to find out the time for which the body remains in the air. So, let us assume the time is “t”. As the body is thrown upward, it is clear that due to gravity it will come back down, thus we can say the body has reached its maximum height. From here, we can conclude that final velocity of the body will be =0 (at its maximum height or its highest point).
The acceleration on the body due to gravity will be = -g because here the body is moving against the gravity i.e. it is moving upward , so we use negative signs to indicate that the body has the opposite direction to gravity. In the question we are given initial velocity (u), final velocity (v), acceleration due to gravity (-g) and we have assumed the time to be (t). As all of these are present in the first equation of motion, we can use the first equation of motion to find out the time for which the body remains in air.
Thus, using first equation of motion,
V= u + a $\times$ t here, acceleration is due to gravity so we will take acceleration as (g).
Final velocity=0
Initial velocity=u
Acceleration due to gravity = -g
Time =t
Substituting the given values in the first equation of motion
So, we get
0 = u + (-g) $\times$ t
$\Rightarrow$ 0 = u – g $\times$ t
From here, t = $\dfrac{u}{g}$
Now, we know the time, but the ball has firstly thrown upward and then it moves down again
So, we have to calculate total time which we can say the time for which the ball remains in air
Total time taken for which the ball remains in air = time of ball going up + time of ball going down = $\dfrac{u}{g} + \dfrac{u}{g} = \dfrac{{2u}}{g}$
Hence, option C is correct.

Note: When in a body there is only gravitational force acting upon it then it is said to be in free fall. For example if we throw a ball vertically upward the ball comes back down because of the gravity acting upon it which brings the ball back to the ground. Thus, we can say that the body in this situation follows the free fall where no other force was acting on the body except the gravity.