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Zolol [24]
3 years ago
14

The closest star to our solar system is Alpha Centauri, which is 4.12 × 10^16 m away. How long would it take light from Alpha Ce

ntauri to reach our solar system if the speed of light is 3.00 × 10^8 m/s? (Provide an answer in both seconds and in years.)
(According to the textbook the answer is 4.35 years, i'm just not sure how to get there as I keep getting a different answer)
Physics
1 answer:
bonufazy [111]3 years ago
4 0

Time = (distance) / (speed)

Time = (4.12x10^16 m) / (3 x10^8 m/s)

Time = 1.37 x 10^8 seconds

Divide the seconds by 86,400 to get days. Then divide the days by 365 to get years.

Time = about 4.35 years

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PLEASE PROVIDE AN EXPLANATION.<br><br> THANKS!!!
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Answer:

(a) A = 0.0800 m, λ = 20.9 m, f = 11.9 Hz

(b) 250 m/s

(c) 1250 N

(d) Positive x-direction

(e) 6.00 m/s

(f) 0.0365 m

Explanation:

(a) The standard form of the wave is:

y = A cos ((2πf) t ± (2π/λ) x)

where A is the amplitude, f is the frequency, and λ is the wavelength.

If the x term has a positive coefficient, the wave moves to the left.

If the x term has a negative coefficient, the wave moves to the right.

Therefore:

A = 0.0800 m

2π/λ = 0.300 m⁻¹

λ = 20.9 m

2πf = 75.0 rad/s

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(b) Velocity is wavelength times frequency.

v = λf

v = (20.9 m) (11.9 Hz)

v = 250 m/s

(c) The tension is:

T = v²ρ

where ρ is the mass per unit length.

T = (250 m/s)² (0.0200 kg/m)

T = 1250 N

(d) The x term has a negative coefficient, so the wave moves to the right (positive x-direction).

(e) The maximum transverse speed is Aω.

(0.0800 m) (75.0 rad/s)

6.00 m/s

(f) Plug in the values and find y.

y = (0.0800 m) cos((75.0 rad/s) (2.00 s) − (0.300 m⁻¹) (1.00 m))

y = 0.0365 m

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