To determine whether the statement is true or false, we need to consider the physics involved in a skater descending a hill.
If a skater starts from rest at the top of a hill and descends, they will convert potential energy at the top into kinetic energy at the bottom. The maximum speed will depend on the height of the hill.
Using the principle of conservation of energy:
\[ PE_{top} = KE_{bottom} \]
Where:
- \( PE_{top} = mgh \) (potential energy at the top)
- \( KE_{bottom} = \frac{1}{2} mv^2 \) (kinetic energy at the bottom)
Assuming no friction or air resistance, if the height of the hill is sufficient, the skater can reach speeds over \( 9.8 , \text{m/s} \).
For example, if the height of the hill is approximately 5 meters:
\[ v = \sqrt{2gh} = \sqrt{2 \times 9.8 , \text{m/s}^2 \times 5 , \text{m}} \approx \sqrt{98} \approx 9.9 , \text{m/s} \]
Thus, with just a hill height of 5 meters, the skater can reach speeds over \( 9.8 , \text{m/s} \).
Therefore, the statement "At the bottom of the hill the skater reaches speeds over 9.8 m/s" is True.