A loaded aeroplane has a total mass of 1.2×105 kg while climbing after take-off. It climbs at an angle of 23°to the horizontal with a speed of 50 m s–1.

Question 14

A loaded aeroplane has a total mass of 1.2×10⁵ kg while climbing after take-off. It climbs at an angle of 23°to the horizontal with a speed of 50 m s–1. What is the rate at which it is gaining potential energy at this time?

A 2.3 × 10⁶ J s^-1

B 2.5 × 10⁶ J s^-1

C 2.3 × 10⁷ J s^-1

D 2.5 × 10⁷ J s^-1

Reference: Past Exam Paper – June 2015 Paper 13 Q18

Solution:

Answer: C.

In this question, we need to manipulate the formulae to obtain quantities with value already given in the question.

Rate of gaining potential energy = Gain in PE / time

GPE = mgh     where h is the vertical height

So, to consider the gain in GPE, we need to consider the vertical component of speed

The aeroplane climbs at a speed of 50 m s^-1 at an angle of 23° to the horizontal.

Vertical component of speed = 50 sin 23°

Rate of gaining potential energy = Gain in PE / time

Rate of gaining potential energy = mgh / t = mg(h/t)

(h/t) is the vertical speed at which the aeroplane climbs.

Rate of gaining potential energy = 1.2×10⁵ × 9.81 × 50 sin23°

Rate of gaining potential energy = 2.3×10⁷ J s^-1