Alion has a mass of 45 kg. answer the following questions about it, using correct units. a. the lion runs at a speed of 14.2 m/s. how much kinetic energy does the lion have? (4 points) b. if the lion runs up a hill to a height of 28 m, how much gravitational potential energy has the lion gained? (4 points) c. a fox with mass 1.8 kg is avoiding a lion by climbing into a tree. the fox climbs to a height of 3.8 m and jumps to another tree at a speed of 8.1 m/s. what is the total mechanical energy of the fox as it jumps? (3 points)

A) The kinetic energy of an object is given by:

where m is the mass of the object, and v its speed. For the lion in our problem, m=45 kg and v=14.2 m/s, so its kinetic energy is


b) the increase in gravitational potential energy of the lion is given by:

where g is the gravitational acceleration, and  is the increase in altitude of the lion. In this problem, , so the increase in gravitational potential energy is


c) When the fox reaches the top of the tree, its gravitational potential energy is

As it jumps, its kinetic energy is

So the total mechanical energy of the fox as it jumps is