a) The kinetic energy of an object is given by:
[tex]K= \frac{1}{2}mv^2 [/tex]
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
[tex]K= \frac{1}{2}mv^2= \frac{1}{2}(45 kg)(14.2 m/s)^2=4537 J [/tex]
b) the increase in gravitational potential energy of the lion is given by:
[tex]\Delta U = mg \Delta h[/tex]
where g is the gravitational acceleration, and [tex]\Delta h[/tex] is the increase in altitude of the lion. In this problem, [tex]\Delta h=28 m[/tex], so the increase in gravitational potential energy is
[tex]\Delta U=mg \Delta h=(45 kg)(9.81 m/s^2)(28 m)=12361 J[/tex]
c) When the fox reaches the top of the tree, its gravitational potential energy is
[tex]U=mgh=(1.8 kg)(9.81 m/s^2)(3.8 m)=67 J[/tex]
As it jumps, its kinetic energy is
[tex]K= \frac{1}{2}mv^2= \frac{1}{2}(1.8 kg)(8.1 m/s)^2=59 J [/tex]
So the total mechanical energy of the fox as it jumps is
[tex]E=U+K=67 J + 59 J =126 J[/tex]
