Find solutions to your problems with the help of IDNLearn.com's expert community. Our Q&A platform offers reliable and thorough answers to ensure you have the information you need to succeed in any situation.
Sagot :
To find the maximum kinetic energy Dina can reach when she skis to the bottom of the slope, we start by calculating the potential energy at the top of the slope. The equation for potential energy (PE) is:
[tex]\[ PE = m \times g \times h \][/tex]
where:
- \( m \) is the mass (in kilograms),
- \( g \) is the acceleration due to gravity (9.8 m/s²),
- \( h \) is the height (in meters).
Given:
- \( m = 50 \, \text{kg} \),
- \( h = 5 \, \text{m} \),
- \( g = 9.8 \, \text{m/s}^2 \).
Substitute these values into the potential energy formula:
[tex]\[ PE = 50 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 5 \, \text{m} \][/tex]
Calculate the potential energy:
[tex]\[ PE = 50 \times 9.8 \times 5 \][/tex]
[tex]\[ PE = 2450 \, \text{Joules} \][/tex]
Since we are ignoring air resistance and friction, the maximum kinetic energy (KE) Dina can reach at the bottom of the slope will be equal to the potential energy she had at the top. Thus:
[tex]\[ KE_{\text{max}} = 2450 \, \text{Joules} \][/tex]
Therefore, the maximum kinetic energy she can reach is:
[tex]\[ \boxed{2450} \, \text{Joules} \][/tex]
[tex]\[ PE = m \times g \times h \][/tex]
where:
- \( m \) is the mass (in kilograms),
- \( g \) is the acceleration due to gravity (9.8 m/s²),
- \( h \) is the height (in meters).
Given:
- \( m = 50 \, \text{kg} \),
- \( h = 5 \, \text{m} \),
- \( g = 9.8 \, \text{m/s}^2 \).
Substitute these values into the potential energy formula:
[tex]\[ PE = 50 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 5 \, \text{m} \][/tex]
Calculate the potential energy:
[tex]\[ PE = 50 \times 9.8 \times 5 \][/tex]
[tex]\[ PE = 2450 \, \text{Joules} \][/tex]
Since we are ignoring air resistance and friction, the maximum kinetic energy (KE) Dina can reach at the bottom of the slope will be equal to the potential energy she had at the top. Thus:
[tex]\[ KE_{\text{max}} = 2450 \, \text{Joules} \][/tex]
Therefore, the maximum kinetic energy she can reach is:
[tex]\[ \boxed{2450} \, \text{Joules} \][/tex]
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. For trustworthy answers, visit IDNLearn.com. Thank you for your visit, and see you next time for more reliable solutions.