Question

If a plane is flying horizontally at $100\;{\text{m}}/{\text{s}}$ at a height of 1000 m releases a bomb from it, then velocity with which the bomb hits the ground is (Let g = 10 $m{s^{ - 2}}$)

A. 72.1 m/s
B. 172.1 m/s
C. 197.2 m/s
D. None of these

Answer 1

Hint: The rate of change of an object's direction with respect to a frame of reference is its velocity, which is a function of time. A definition of an object's speed and direction of travel (e.g. 60 km/h to the north) is equal to velocity. In kinematics, the branch of classical mechanics that explains the motion of bodies, velocity is a central term.

Formula used:
${v^2} = {u^2} + 2gs$
V = final velocity
U = initial velocity
G = acceleration due to gravity
S = displacement

Complete step-by-step answer:
Equations of motion are physics equations that define a physical system's action in terms of its motion as a function of time. The equations of motion, more precisely, describe the behaviour of a physical system as a sequence of mathematical functions expressed in terms of dynamic variables. Typically, these variables are spatial coordinates and time, but they can also contain momentum components. Generalized coordinates are the most versatile choice, since they can be any convenient physical device component.
Now Given data
${u_{horizontal}}$=1000 m/s
${u_{vertical}}$ = 0 m/s
V = ?
G = 10 $m{s^{ - 2}}$
S =100 m
Substituting all in the given formula we get
${v^2} = {u^2} + 2gs$

${v^2} = 0 + 2 \times 10 \times 1000$
${v^2} = 20000$
$v = 100\sqrt 2 \hat j$
Hence
Net velocity = $\hat u + \hat v$
Net velocity = $100\widehat {i} + 100\sqrt 2 \hat j$
Using Vector properties
= 100$\sqrt {1 + 2} $
= $100\sqrt 3 $
= 172.1 m/s

So, the correct answer is “Option C”.

Note: There are two types of motion descriptions: dynamics and kinematics. Since the momenta, forces, and energy of the particles are taken into consideration, dynamics is broad. In this case, the term dynamics can refer to both the system's differential equations (such as Newton's second law or the Euler–Lagrange equations) and the solutions to those equations.