Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Given:
The proper length of the sports car is: L₀ = 5.9 m
The contracted length of the sports car is: L = 5.4 m
To find:
The speed of the car.
Explanation:
The length contraction is the shortening of the length of the moving object as measured relative to the observer's frame of reference.
The expression for length contraction is given as:
[tex]L=L_0\sqrt{1-\frac{v^2}{c^2}}[/tex]Here, L is the contracted length, L₀ is the proper length, v is the speed of the object and c is the speed of light having a value 3 × 10⁸ m/s.
Substituting the values in the above equation, we get:
[tex]\begin{gathered} 5.4\text{ m}=5.9\text{ m}\sqrt{1-\frac{v^2}{c^2}}\text{ } \\ \\ \frac{5.4\text{ m}}{5.9\text{ m}}=\sqrt{1-\frac{v^2}{c^2}} \\ \\ (\frac{5.4\text{ m}}{5.9\text{ m}})^2=1-\frac{v^{2}}{c^{2}} \\ \\ \frac{v^{2}}{c^{2}}=1-(\frac{5.4\text{ m}}{5.9\text{ m}})^2 \\ \\ v^2=c^2(1-(\frac{5.4\text{ m}}{5.9\text{ m}})^2) \\ \\ v=\sqrt{c^2(1-(\frac{5.4\text{ m}}{5.9\text{ m}})^2)} \\ \\ v=c\sqrt{1-\frac{(5.4\text{ m\rparen}^2}{(5.9\text{ m\rparen}^2}} \\ \\ v=c\times0.40 \\ \\ v=0.40c \end{gathered}[/tex]Final answer:
The sports car should travel with a speed of 0.40c so that the length of the car appears to be 5.4 m.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
