Final answer:
To make a 6.0 m-long sports car appear only 5.5 m long, it must travel at a velocity of 0.200 times the speed of light, which is option (b) 0.200c.
Step-by-step explanation:
The question is about the phenomenon known as length contraction in special relativity. To find out how fast a 6.0 m-long sports car needs to travel to appear as 5.5 m long, we can use the length contraction formula:
L = L0 * √(1 - v^2/c^2)
Where:
- L is the contracted length (5.5 m in this case).
- L0 is the proper length (6.0 m).
- v is the velocity of the object.
- c is the speed of light in a vacuum (approximately 3.00 x 10^8 m/s).
We need to solve for v:
5.5 m = 6.0 m * √(1 - v^2/c^2)
By squaring both sides and then rearranging for v, we calculate that the velocity v works out to be 0.200c, which corresponds to answer option (b) 0.200c.