Question

A rocket of 3 x 10⁶ mass takes off from a launching pad and acquires a vertical velocity of 1 km/s at an altitude of 25 km.

Calculate (a) the potential energy, (b) the kinetic energy.
(Take the value of g = 10 m/s2)

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Answer 1

Given :-

Mass of the rocket = 3 × 10⁶ kg

Velocity of the rocket = 1 km/s

Altitude of the rocket = 25 km

To Find :-

The potential energy of the rocket.

The kinetic energy of the rocket.

Solution :-

We know that,

• PE = Potential energy
• m = Mass
• h = Height
• g = Gravity
• KE = Kinetic energy
• v = Velocity

Using the formula,

$\underline{\boxed{\sf Potential \ energy=Mass \times Gravity \times Height}}$

Given that,

Mass (m) = 3 × 10⁶ kg

Gravity (g) = 10 m/s

Height (h) = 25 km = 25000 m

Substituting their values,

⇒ PE = mgh

⇒ PE = 3 × 10⁶ × 10 × 25000

⇒ PE = 750000000000 = 7.5 × 10¹¹

Therefore, the potential energy of the rocket is 7.5 × 10¹¹.

Using the formula,

$\underline{\boxed{\sf Kinetic \ energy= \dfrac{1}{2} mv^2}}$

Given that,

Mass (m) = 3 × 10⁶ kg

Velocity (v) = 1 km/s = 1000 m/s

Substituting their values,

⇒ KE = 1/2 × 3 × 10⁶ × 1000²

⇒ KE = 3 × 10⁶ × 1000² / 2

⇒ KE = 1.5 × 10¹² J

Therefore, the kinetic energy of the rocket is 1.5 × 10¹² J.

Answer 2

Answer:

Given, mass of the rocket, m=3×106kg ;

velocity of the rocket, v=1km/s=1000m/s ;

Kinetic energy of the rocket, Ek=21mv2

=21(3×106)(1000)2=1.5×1012J