Question

What is the work done by an aeroplane flying at 180 km/h to increase its speed to 270 km/h ? Take mass of aeroplane as 20,000kg.

(a) 31,000 J
(b) 25,000 J
(c) 31,250 J
(d) 31,250,000 J

ANSWER FROM THE OPTIONS ONLY

Answer 1

Given :-

Final velocity of the aeroplane = 270 km/h

Initial velocity of the aeroplane = 180 km/h

Mass of the aeroplane = 20000 kg

To Find :-

The work done by an aeroplane.

Analysis :-

Here we are given with the final velocity, initial velocity and mass of the aeroplane.

In order to find the work done substitute the values accordingly such that, kinetic energy is equal to one by two multiplied by mass multiplied by velocity square.

Solution :-

We know that,

• m = Mass
• u = Initial velocity
• KE = Kinetic energy
• v = Final velocity

According to the question,

Since the initial and final velocity is given, substitute the values accordingly showing it's difference in the formula.

Using the formula,

$\underline{\boxed{\sf Kinetic \ energy=\dfrac{1}{2} m (v^2-u^2) }}$

Given that,

Mass (m) = 20000 kg

Initial velocity (u) = 180 km/h = 50 m/s

Final velocity (v) = 270 km/h = 75 m/s

Substituting their values,

⇒ KE = 1/2 × 20000 × (75² - 50²)

⇒ KE =  1/2 × 20000 × (5625 - 2500)

⇒ KE =  1/2 × 20000 × 3125

⇒ KE = 20000 × 3125 / 2

⇒ KE = 62500000 / 2

⇒ KE = 31250000 J

Therefore, the work done by the aeroplane is (d) 31,250,000 J.

Answer 2

Given :-

• Final velocity of the aeroplane = 270 km/h

• Initial velocity of the aeroplane = 180 km/h

• Mass of the aeroplane = 20000 kg

To Find :-

The work done by an aeroplane.

Analysis :-

Here we are given with the final velocity, initial velocity and mass of the aeroplane.

In order to find the work done substitute the values accordingly such that, kinetic energy is equal to one by two multiplied by mass multiplied by velocity square.

Solution :-

We know that,

• m = Mass
• u = Initial velocity
• KE = Kinetic energy
• v = Final velocity

According to the question,

Since the initial and final velocity is given, substitute the values accordingly showing it's difference in the formula.

Using the formula,

Kinetic energy= 1/2 m(v²−u² )

Given that,

Mass (m) = 20000 kg

Initial velocity (u) = 180 km/h = 50 m/s

Final velocity (v) = 270 km/h = 75 m/s

Substituting their values,

⇒ KE = 1/2 × 20000 × (75² - 50²)

⇒ KE = 1/2 × 20000 × (5625 - 2500)

⇒ KE = 1/2 × 20000 × 3125

⇒ KE = 20000 × 3125 / 2

⇒ KE = 62500000 / 2

⇒ KE = 31250000 J

Therefore, the work done by the aeroplane is (d) 31,250,000 J.