Question

The superheroine Xanaxa, who has a mass of 68.1 kg , is pursuing the 75.3 kg archvillain Lexlax. She leaps from the ground to the top of a 193 m high building then dives off it and comes to rest at the bottom of a 16.1 m deep excavation where she finds Lexlax and neutralizes him. Does all this bring about a net gain or a net loss of gravitational potential energy?

Answer 1

The concept required to solve this problem is associated with potential energy. Recall that potential energy is defined as the product between mass, gravity, and change in height. Mathematically it can be described as

$U = mg\Delta h$

Here,

$\Delta h$ = Change in height

m = mass of super heroine

g = Acceleration due to gravity

The change in height will be,

$\Delta h = h_f - h_i$

The final position of the heroin is below the ground level,

$h_f = -16.1m$

The initial height will be the zero point of our system of reference,

$\Delta h = -16.1m-0m$

$\Delta h = -16.1m$

Replacing all this values we have,

$U = mg\Delta h$

$U = (68.1kg)(9.8m/s^2)(-16.1m)$

$U = -10744.81J$

Since the final position of the heroine is located below the ground, there will net loss of gravitational potential energy of 10744.81J