Question

actice Problems 4
1. An aeroplane on a runway, starts from rest and picks up a velocity of 180 km/h and takes off.
In doing so, it covers a runway of 1.5 km. Calculate (i) the uniform acceleration acting on the
aeroplane and (ii) the time in which it takes off.
​

Answer 1

Given data :-

• An aeroplane on a runway, starts from rest and picks up a velocity of 180 km/hr.
• An aeroplane covers a runway of 1.5 km.

Solution :-

Here,

u = initial velocity, v = final velocity, a = acceleration of the particle, t = time taken by particle, s = displacement of the particle.

{According to given}

→ An Aeroplane's initial velocity ( u ) = 0

{because aeroplane at rest}

→ An Aeroplane's final velocity ( v ) = 180km/hr

→ Displacement of an aeroplane ( s ) = 1.5 km

Here we use kinematical equation to find acceleration acting on the aeroplane.

→ v² = u² + 2as

→ v² - u² = 2as

→ 180 - 0 = 2 × a × 1.5

→ 180 = 3 × a i.e.

→ a = 180/3

→ a = 60 km/hr²

{ Note :-

→ 60 km/hr² = [(60×1000)/(60×60)²] m/s²

→ 60 km/hr² = [(60000)/(3600)²] m/s²

→ 60 km/hr² =[60000/12960000] m/s²

→ 60 km/hr² = [1/216] m/s²

→ 60 km/hr² = 0.0046 m/s² }

Now to find the time in which aeroplane takes off. { we use formula of velocity }

→ Velocity = Displacement/Time

→ Time = Displacement/Velocity

→ Time = 1.5/180

→ Time = 1/120

→ Time = 0.0083 hr

{Note :-

→ 0.0083 hr = [0.0083 × ( 60 × 60 ) ] sec

→ 0.0083 hr = [0.0083 × 3600 ] sec

→ 0.0083 hr = 29.88 sec }

Hence,

( i ) The uniform acceleration acting on the aeroplane is 60 km/hr². and

( ii ) The time in which aeroplane takes off is 0.0083 hr.