Question

A lion 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)

Answer 1

a. v = 14.91 m/s

b. 12, 361 J

c. 8.1 m/s

Step-by-step explanation:

Alternate A P E X answers

Answer 2

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

`K= (1)/(2)mv^2`
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

`K= (1)/(2)mv^2= (1)/(2)(45 kg)(14.2 m/s)^2=4537 J`

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

`\Delta U = mg \Delta h`
where g is the gravitational acceleration, and
`\Delta h` is the increase in altitude of the lion. In this problem,
`\Delta h=28 m`, so the increase in gravitational potential energy is

`\Delta U=mg \Delta h=(45 kg)(9.81 m/s^2)(28 m)=12361 J`

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

`U=mgh=(1.8 kg)(9.81 m/s^2)(3.8 m)=67 J`
As it jumps, its kinetic energy is

`K= (1)/(2)mv^2= (1)/(2)(1.8 kg)(8.1 m/s)^2=59 J`
So the total mechanical energy of the fox as it jumps is

`E=U+K=67 J + 59 J =126 J`