## College Physics (4th Edition)

Published by McGraw-Hill Education

# Chapter 14 - Problems - Page 534: 16

#### Answer

If 3.3% of the energy from the food could be converted into gravitational potential energy in a single jump, the athlete could jump to a height of $705~m$

#### Work Step by Step

We can convert the energy to units of joules: $3000~kcal\times \frac{4186~J}{1~kcal} = 1.2558\times 10^7~J$ We can find the amount of energy that can be converted into gravitational potential energy: $(0.033)(1.2558\times 10^7~J) = 4.14414\times 10^5~J$ We can find the height the athlete could jump: $U_g = 4.14414\times 10^5~J$ $mgh = 4.14414\times 10^5~J$ $h = \frac{4.14414\times 10^5~J}{mg}$ $h = \frac{4.14414\times 10^5~J}{(60.0~kg)(9.80~m/s^2)}$ $h = 705~m$ If 3.3% of the energy from the food could be converted into gravitational potential energy in a single jump, the athlete could jump to a height of $705~m$

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