Question

An engine of a jet aircraft applies a thrown force of ${{10}^{5}}N$ during takeoff and causes the plane to attain a velocity of $1\text{ km/s}$in 10 seconds. The mass of the plane is:
A. ${{10}^{2}}\text{ kg}$
B. ${{10}^{3}}\text{ kg}$
C. ${{10}^{4}}\text{ kg}$
D. ${{10}^{5}}\text{ kg}$

Answer 1

Hint: The thrown force in the problem produces an upward thrust to the jet, which will accelerate it. The force applied to the jet aircraft will be equal and opposite to the thrown force produced by the engine. The aircraft is initially at rest, the force acting on the aircraft will accelerate it, and the mass can be found out if we know the acceleration.
Formula Used:
Newton’s formula for motion, for a body which has an initial velocity u and final velocity v and having an acceleration a in a time period t is given by,
$v=u+at$
From Newton’s second law, the force acting on a body is the product of its mass and acceleration. So, we can write,
$F=ma$

Complete step by step answer:
The thrown force produced by the aircraft engine is ${{10}^{5}}N$. It takes the jet aircraft 10 seconds to attain a velocity of $1\text{ km/s}$ starting from rest. So, the acceleration produced in this case can be found out by using the formula, $v=u+at$, in this case, u is zero, a is the acceleration of the body, t is the time taken, and v is the final velocity. So, substituting the values in the equation is,
$1000m{{s}^{-1}}=a\left( 10s \right)$
$\Rightarrow a=\dfrac{1000m{{s}^{-1}}}{10s}$
$\therefore a=100m{{s}^{-2}}$
From Newton’s second law, the force acting on a body is the product of its mass and acceleration. So, we can write,
$F=ma$
$m=\dfrac{F}{a}$
Substituting the values of F and a, we get,
$m=\dfrac{{{10}^{5}}N}{{{10}^{2}}m{{s}^{-2}}}$
$\therefore m={{10}^{3}}kg$
So, the mass of the jet aircraft is ${{10}^{3}}kg$.
So, the answer to the question is option (B).
Note:
Newton’s Third law states that ‘For every action, there is an equal and opposite reaction’ or we can say that that, all forces between two objects exist in equal magnitude and in the opposite direction.
If we take the example of the apple and the earth, the earth applies a gravitational force on the apple which applies a downwards acceleration on the apple, at the same time due to a reaction force, the earth is also accelerated towards the apple, but due to the huge mass of the earth compared to the mass of the apple, the acceleration produced is negligible.