9702/May Jun/13/2015/Q18

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

Solution:

Answer: C.

sin 23^o = y/50

y = 50 sin 23^o

    = 19.54 ms^-1

Use v² = u² + 2as to find the h

19.54² = 0 + 2 (9.81) S

S = 19.46 m

P.E. = mgh

        = (1.2 x 10⁵ )(9.81)(19.46)

         = 2.29 x 10⁷ Js^-1

Reference: PYQ - May/Jun 2015 Paper 13 Q18