Question

A body is projected vertically upwards with a velocity u. It crosses a point in its journey at a height h meter twice, just after 1 and 7 seconds .The value of u in m/s is ($g=10m/{{s}^{2}}$)
A: 50
B: 40
C: 30
D: 20

Answer 1

A body that is projected upwards will definitely experience freefall due to the force of gravity. In the given scenario, there is no mention of any kind of external forces that act on the body. The only force that acts here is the force due to gravity. This point must be remembered while approaching the question.

Complete step by step answer:
In the question, we are given a body that is projected upwards with an initial velocity of value u. It is also said that the body crosses the same point at the same height after the first second and the seventh second.

Here, in order to find the value of u, we can use the equation of motion, that is
$h=ut-\dfrac{1}{2}g{{t}^{2}}$, where h is the height, t is the time and g is the acceleration due to gravity.
$\begin{aligned}
& h=u(1)-\dfrac{1}{2}g=u-\dfrac{g}{2}.............(1) \\
& h=u(7)-\dfrac{{{7}^{2}}}{2}g=7u-\dfrac{49g}{2}.............(2) \\
& 1\And 2\Rightarrow \\
& u-\dfrac{g}{2}=7u-\dfrac{49g}{2} \\
& 24g=6u \\
& u=4g \\
& \Rightarrow u=40m/s \\
\end{aligned}$$$

Hence, option B is the correct answer among the given options.

Note: Here, acceleration due to gravity is given a negative sign as the body is drawn towards the earth in the downward direction due to the gravitational force that acts on the body. The mass of the body is not given importance here as the body becomes massless when it undergoes freefall. Thus, the mass is neglected.