Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Discover a wealth of knowledge from professionals across various disciplines on our user-friendly Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
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]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.