Question

An airplane requires a speed of $108$ kmph to take off, to achieve that plane runs on the runway of $100$m. Mass of the plane is $10400$kg and the coefficient of friction between the plane and the ground is $0.2$. Assuming the plane accelerates uniformly, the minimum force required is $($Take g $= 9.8$ m$9.8m/{s^2})$
A. $2 \times {10^4}N$
B. $2.43 \times {10^4}N$
C. $6.72 \times {10^4}N$
D. $8.86 \times {10^4}N$

Answer 1

To solve this problem we have to know about acceleration. What is acceleration? Acceleration is the rate of change of velocity. That means we can say, acceleration is equal to velocity upon time. when acceleration becomes negative then it is called retardation. Retardation is exactly the same thing as acceleration but in the opposite direction. So, we can say that acceleration makes an object more speedy and retardation helps an movable object to stop.

Complete step by step answer:
We know that, the required take off speed is $108$ kmph which is equal to $30m/s$ over a run of $100$ m .We know that,
${v^2} - {u^2} = 2as$
$\Rightarrow{v^2} - 0 = 2as$
$\Rightarrow a = \dfrac{{{v^2}}}{{2s}}$
So, we know that a is the acceleration. U is equal to initial velocity and v is final velocity.
We are considering here F is equal to force which should be developed by the engine is given by
$F - \mu mg = ma$
$\Rightarrow F = 0.2(10400)(9.81) + 10400(\dfrac{{{{30}^2}}}{{2(100)}}) \\\ \therefore F = 6.72 \times {10^4}N \\\$
So, the right option will be option C.

Note: We can get confused between initial velocity and final velocity. Sometimes we may worry about which value we should put for initial velocity. But we have to keep in our mind that, if any object starts their movement from resting position then obviously the initial velocity is null which is zero.