Question

A boy wants to jump from building $A$ to building $B$. Height of the building $A$ is $25m$ and that of building $B$ is $5m$.Distance between buildings is $4m$.Assume that the body jumps horizontally, then calculate minimum velocity with which he has to jump to land safely on building $B$.

A. $6m/s$
B. $8m/s$
C. $4m/s$
D. $2m/s$

Answer 1

In this question, first we will discuss about the second law of equation of motion and then find the time taken to jump and then use the horizontal distance to calculate the minimum velocity required to jump safely from building $A$ to building $B$.

Complete step by step answer:
It is given that the boy wants to jump from building $A$ to building $B$.The height of the building $A$ is $25m$ and the height of the building $B$ is $5m$. The distance between the two buildings is $4m$.The boy jumps horizontally.Let say the boy jumps at a velocity $Vm/s$.Hence the vertical velocity of the boy is $0$ and the horizontal velocity is $Vm/s$ as the boy jumps horizontally.
Now the vertical distance between the two buildings is $25 - 5 = 20m$.
So we know the second law of equation of motion $S = ut + \dfrac{1}{2}a{t^2}$ [where $S$ is the distance, $u$ is the initial velocity, $t$ is time and $a$ is acceleration due to gravity]
So the initial velocity of the boy is $0$, $a = 10m/{s^2}$, $S = 20m$ the distance boy has to jump.
$20 = 0 \times t + \dfrac{1}{2} \times 10{t^2}$
After simplification we will get,
$t = 2s$
The boy needs $2\sec$to jump from building $A$ to building $B$.Now the horizontal distance is $4m$and the horizontal velocity is $Vm/s$.
So, we can say that
$Vt = 4 \\\ \Rightarrow V = \dfrac{4}{t} \\\ \Rightarrow V= \dfrac{4}{2}\\\ \therefore V= 2m/s$
So the minimum velocity to jump safely from $A$ to building $B$ is required $2m/s$.

Hence option (D) is correct.

Note: As we know that acceleration is a vector quantity that has magnitude and direction. As the boy is falling down so the acceleration due to gravity is in the same direction of gravity so here acceleration is taken as positive.