Question

Consider a 12.5 kg baby tiger in a tree has 490 J of gravitational potential energy. Determine the height of the tiger above the ground?

Answer 1

`\boxed {\boxed {\sf 4 \ meters}}`

Step-by-step explanation:

Gravitational potential energy can be found using the following formula:

`E_P=m*g*h`

where m is the mass, g is the gravitational acceleration, and h is the height.

The mass of the tiger is 12.5 kilograms. The gravitational acceleration on Earth is 9.8 m/s².

• The potential energy is 490 Joules.
• Convert the units to simplify cancelling units later.
• 1 Joule is equal to 1 kilogram * meter² /second²
• Our answer of 490 J = 490 kg*m²/s²

`m= 12.5 \ kg \\g= 9.8 \ m/s^2\\E_p= 490 \ kg*m^2/s^2`

Substitute the values into the formula.

`490 \ kg*m^2/s^2 = 12.5 \ kg * 9.8 \ m/s^2 *h`

Multiply 12.5 kg and 9.8 m/s²

• 12.5 kg* 9.8 m/s² = 122.5 kg*m/s²

`490 \ kg*m^2/s^2 = 122.5 \ kg *m/s^2 *h`

Since we are trying to solve for h, we must isolate it. Since h is being multiplied by 122.5, we must divide both sides by that number because the inverse of division is the inverse of multiplication.

`\frac{490 \ kg*m^2/s^2} { 122.5 \ kg *m/s^2}= ( 122.5 \ kg *m/s^2 *h )/( 122.5 \ kg *m/s^2)`

Note that when dividing, the kg*m/s² will cancel each other out, but a m (meter) will be left.

`(490 \ m )/(122.5) =h`

`4 \ m =h`

The tiger was 4 meters above the ground.