Question

ed ted ted (7%) Problem 5: The parameter y= 1/(1-²) can be used to determine how large relativistic effects can be expected to be. When the speed is small compared to the speed of light, y does not get much larger than 1. As v gets close to the speed of light, y gets very large. Randomized Variables p=0.035 At what speed, as a ratio to the speed of light, is y=1+0.035? This corresponds to a 0.035 x 100 percent relativistic effect. v/c= 05 Grade Summary Deductions Potential Late Work 100% 50% sin() cos() tan()) ( 7 8 9 HONE Late Potential 50% cotan() asin() acos() EM4 5 6 atan() acotan() sinh() 1 2 3 Submissions Attempts remaining: 40 (0% per attempt) detailed view cosh() + 3 0 tanh() cotanh() Degrees O Radians Vo Submit Hint I give up! Hints: 0% deduction per hint. Hints remaining 1 Feedback: 3% deduction per feedback.

Answer 1

To find the speed, as a ratio to the speed of light, at which y = 1 + 0.035, we can solve the equation:

y = 1 / sqrt(1 - (v/c)^2) = 1 + 0.035

Let's solve this equation for v/c:

1 / sqrt(1 - (v/c)^2) = 1 + 0.035

Now, we can simplify the equation by squaring both sides:

1 = (1 + 0.035)^2 * (1 - (v/c)^2)

Expanding and rearranging the equation:

1 - (v/c)^2 = (1 + 0.035)^2

(v/c)^2 = 1 - (1 + 0.035)^2

(v/c)^2 = 1 - (1.035)^2

(v/c)^2 = 1 - 1.070225

(v/c)^2 = -0.070225

Now, we can take the square root of both sides:

v/c = sqrt(-0.070225)

Since the square root of a negative number is not defined in the real number system, it means that there is no real solution for v/c in this case. Therefore, there is no speed, as a ratio to the speed of light, at which y = 1 + 0.035.