Question

An aeroplane taking off from a field has a run of 500 m . What is the acceleration and take off velocity if it leaves the ground 10 seconds after the start ?

Answer 1

QueStI0N -

An aeroplane taking off from a field has a run of 500 m .

What is the acceleration and take off velocity if it leaves the ground 10 seconds after the start ?

SoLuTiOn -

In the above Question , the following information is given -

The length of the runway is 500 m .

The aeroplane leaves the ground 10 seconds after the start .

So,

The speed of the aeroplane while on the ground -

=> ( 500 m / 10 s ) = 50 m/s .

Now, Let us find the acceleration of the plane .

According to the Second Equation Of Motion -

S = ut + ( 1/2 ) at^2 .

The plane is innitially at rest.

So, u = 0

=> 500 = ( 1 / 2 ) × a × 100

=> Acceleration = 10 m/s .

Now according to the First Equation Of Motion -

v = u + at

=> v = 0 + 100

=> v = 100 m/s.

So, the required velocity of the plane when it just leaves the ground is 100 m/s .

Answer 2

GiveN :-

♦ Distance travelled, s = 500 m

♦ Initial velocity, u = 0 m/s    〘As the aeroplane starts from rest〙

♦ Time, t = 10 s

TO FinD :-

The acceleration and the take off velocity of the aeroplane.

AcknowledgemenT :-

♦ s = ut + 1/2 at²

$\textsl{Where,}$

• s is the distance travelled.

• u is the initial velocity

• t is the time taken

• a is the acceleration

♦ v = u + at

$\textsl{Where,}$

• v is the final velocity.

• u is the initial velocity

• a is the acceleration

• t is the time taken

SolutioN :-

$\sf{s = ut + \dfrac{1}{2} at\²}$

$\textsl{Putting the values :-}$

$\sf{\implies 500=0(10)+\dfrac{1}{2}a(10)^2}\\\\\sf{\implies 500=0+\dfrac{100a}{2}}\\\\\sf{\implies 500=50a}\\\\\sf{\implies a=\dfrac{500}{50}}\\\\\underline{\boxed{\sf{\implies a=10\ m/s^2}}}$

$\rule{150}{2}$

$\sf{v=u+at}$

$\textsl{Putting the values :-}$

$\sf{\implies v=0+(10)(10)}\\\\\sf{\implies v=(10)^2}\\\\\underline{\boxed{\sf{\implies v=100\ m/s}}}$

Therefore, the acceleration and the take off velocity of the aeroplane are 10 m/s² and 100 m/s respectively.