Question

Jai is standing on the top of a building of height 25m. He wants to throw his gun to Veeru who stands on top of another building of height 20m at distance 15m from the first building. For which horizontal speed of projection, it is possible?

Answer 1

Apply a second equation of motion for finding time to travel horizontal speed, with the help of this calculate speed for throwing a gun from a building of height 25m to another building of height 20m.

Formula used:
$s = ut + \dfrac{1}{2}a{t^2}$

Complete step by step solution:

As shown in the figure, the first building where jai stands has 5m extra height by comparing another building of height where veeru stands.
$s = ut + \dfrac{1}{2}a{t^2}$
$s$ is distance.
$u$ is the initial velocity.
$t$ is the interval of time.
$a$ is the acceleration.
We take s=-5, u=0, a=-g
-5=-$\dfrac{1}{2}$g${t^2}$
$t = \sqrt {\dfrac{{10}}{{10}}}$
$\Rightarrow t = 1$sec this is time taken for the gun to travel equal height of the building i.e 20m.
By putting above value in the formula with ${t^2}$=0
$ut = 15 \\\ \Rightarrow u = 1 \times 15 \\\ \therefore u = 15m/\sec \\\$

Hence jai throw a gun with the speed of $15m/sec$ then it is possible.

Additional information:
$\bullet$ Speed is the scalar quantity. We can define it as distance travelled per unit time.
$\bullet$ Acceleration is vector quantity. We can define its rate of change of velocity.
$\bullet$ In the question, horizontal speed means the gun travels in x-direction or side by-side.
$\bullet$ The unit of speed is m/sec.
$\bullet$ We must remember all three equations of motion $v=u+at$, ${{v^2}={u^2}+2as}$, $s$=$ut$+$\dfrac{1}{2}at^2$ to get more marks.
$\bullet$ Initial velocity is nothing but velocity at the time interval is 0, which is denoted by u.
$\bullet$ Final velocity is nothing but velocity which the body has at the end of the given time period.

Note:
If possible draw a diagram clearly for better understanding of the given question. If you make any mistakes in the diagram we will get the wrong answer. So, students must be careful while making the diagram.