Answer :
We start with the formula for gravitational potential energy:
[tex]$$
PE = mgh,
$$[/tex]
where
- [tex]$PE$[/tex] is the potential energy,
- [tex]$m$[/tex] is the mass,
- [tex]$g$[/tex] is the acceleration due to gravity, and
- [tex]$h$[/tex] is the height from the floor.
The given values are:
[tex]$$
PE = 196 \text{ Joules}, \quad m = 5 \text{ kg}, \quad g = 9.8 \text{ m/s}^2.
$$[/tex]
To find the height [tex]$h$[/tex], we solve for [tex]$h$[/tex] by rearranging the equation:
[tex]$$
h = \frac{PE}{mg}.
$$[/tex]
Substitute the given numbers into the equation:
[tex]$$
h = \frac{196}{5 \times 9.8}.
$$[/tex]
Calculate the product in the denominator:
[tex]$$
5 \times 9.8 = 49.
$$[/tex]
Now compute the height:
[tex]$$
h = \frac{196}{49} = 4 \text{ meters}.
$$[/tex]
Thus, the book is [tex]$4$[/tex] meters from the floor.
[tex]$$
PE = mgh,
$$[/tex]
where
- [tex]$PE$[/tex] is the potential energy,
- [tex]$m$[/tex] is the mass,
- [tex]$g$[/tex] is the acceleration due to gravity, and
- [tex]$h$[/tex] is the height from the floor.
The given values are:
[tex]$$
PE = 196 \text{ Joules}, \quad m = 5 \text{ kg}, \quad g = 9.8 \text{ m/s}^2.
$$[/tex]
To find the height [tex]$h$[/tex], we solve for [tex]$h$[/tex] by rearranging the equation:
[tex]$$
h = \frac{PE}{mg}.
$$[/tex]
Substitute the given numbers into the equation:
[tex]$$
h = \frac{196}{5 \times 9.8}.
$$[/tex]
Calculate the product in the denominator:
[tex]$$
5 \times 9.8 = 49.
$$[/tex]
Now compute the height:
[tex]$$
h = \frac{196}{49} = 4 \text{ meters}.
$$[/tex]
Thus, the book is [tex]$4$[/tex] meters from the floor.
