To determine the maximum kinetic energy Dina can reach when she skis to the bottom of the slope, we need to calculate her potential energy at the top of the slope. This potential energy will be equal to the kinetic energy at the bottom of the slope, assuming no energy losses due to air resistance or friction.
Given:
- Mass ([tex]\( m \)[/tex]) = 50 kilograms
- Gravitational acceleration ([tex]\( g \)[/tex]) = 9.8 meters per second squared
- Height ([tex]\( h \)[/tex]) = 5 meters
First, we use the formula for potential energy:
[tex]\[ PE = m \times g \times h \][/tex]
Now, let's substitute the given values into the formula:
[tex]\[ PE = 50 \times 9.8 \times 5 \][/tex]
Calculating this step-by-step:
1. [tex]\( 50 \times 9.8 = 490 \)[/tex]
2. [tex]\( 490 \times 5 = 2450 \)[/tex]
Thus, the potential energy at the top of the slope is 2450 joules.
Since the potential energy at the top of the slope will be converted into kinetic energy at the bottom of the slope:
The maximum kinetic energy she can reach when she skis to the bottom of the slope is [tex]\( \boxed{2450} \)[/tex] joules.
