Galileo attempted to measure the speed of light by measuring the time elapsed between his opening a lantern and his seeing the light return from his assistant's lantern. What distance, d, must separate Galileo and his assistant in order for the human reaction time, Δt = 0.2 s, to introduce no more than a 14 % error in the speed of light? Answer in meters.

Respuesta :

Answer:

The distance is [tex]2.58\times10^{7}\ m[/tex].

Explanation:

Given that,

Time [tex]\Delta t = 0.2\ s[/tex]

The velocity is no more than a 14 % error in the speed of light.

So,

Velocity [tex]v= c\times 86\%[/tex]

We need to calculate the distance

Using formula of speed

[tex]v = \dfrac{d}{t}[/tex]

[tex]d = v\times t[/tex]

Where, v = speed

d = distance

t = time

Put the value into the formula

[tex]d = 3\times10^{8}\times\dfrac{86}{100}\times0.2[/tex]

[tex]d=516\times10^{5}\ m[/tex]

We know that,

The one side distance d' is

[tex]d'=\dfrac{d}{2}[/tex]

[tex]d'=\dfrac{516\times10^{5}}{2}[/tex]

[tex]d'=2.58\times10^{7}\ m[/tex]

Hence, The distance is [tex]2.58\times10^{7}\ m[/tex].

The distance in this scenario is 2.58 × 10⁷ m.

What is Distance?

This is defined as the amount of space between two points or lines.

Δt = 0.2s

Velocity = no more than a 14 % error in the speed of light = c × 86%

Distance = velocity/time

3× 10⁸ × 86/100 × 0.2

= 516 × 10⁵ m

Since only one side is involved

516 × 10⁵ /2 = 2.58 × 10⁷ m.

Read more about Distance here https://brainly.com/question/17273444