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Chapter 31: Problem 54

A laser beam takes 50.0 ms to be reflected back from a totally reflecting sail on a spacecraft. How far away is the sail?

Short Answer

Expert verified
Answer: The distance between the laser source and the reflecting sail is \(7.50 \times 10^6\) meters.

Step by step solution

01

Convert time to seconds

The time is given in milliseconds (ms), so we first need to convert it to seconds (s) using this conversion factor: 1 s = 1000 ms So, 50.0 ms = 50.0/1000 s = 0.050 s.
02

Write down the speed of light

The speed of light \(c\) in a vacuum is approximately: \(c = 3.00 \times 10^8\) m/s.
03

Calculate the total distance the light travels

The laser beam travels to the sail and back; thus, it covers twice the distance between the source and the sail. We can find the total distance traveled by the light using the formula: distance = speed x time total distance = \(c \times t\), where \(t\) is the time taken by the light. total distance = \((3.00 \times 10^8 \text{ m/s}) \times (0.050 \text{ s})\) total distance = \(1.50 \times 10^7\) m
04

Find the distance between the laser source and the sail

Since the laser beam travels to the sail and back, the distance to the sail is half of the total distance the light travels. Therefore: distance to the sail = total distance / 2 distance to the sail = \((1.50 \times 10^7 \text{ m}) / 2\) distance to the sail = \(7.50 \times 10^6\) m So, the distance between the laser source and the reflecting sail is \(7.50 \times 10^6\) meters.

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Most popular questions from this chapter

A \(14.9-\mu F\) capacitor, a \(24.3-\mathrm{k} \Omega\) resistor, a switch, and a 25.-V battery are connected in series. What is the rate of change of the electric field between the plates of the capacitor at \(t=0.3621 \mathrm{~s}\) after the switch is closed? The area of the plates is \(1.00 \mathrm{~cm}^{2}\) .

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