Question

Radio Waves Radio waves travel at the same speed as light, \(3.0 \times 10^{8}\) meters per second. Find the time required for a radio wave to travel from mission control in Houston to NASA astronauts on the surface of the moon \(3.84 \times 10^{8}\) meters away.

Short answer

It takes about 1.28 seconds for a radio wave to travel from mission control in Houston to NASA astronauts on the surface of the moon.

Step-by-step solution

Identify the given values

The speed of radio waves is the same as the speed of light, which is \(3.0 \times 10^{8}\) meters per second. The distance they need to cover is \(3.84 \times 10^{8}\) meters.

Use the speed formula to compute the time

Speed is equal to distance traveled divided by time. To find the time, one can rearrange this equation. The rearranged equation to solve for time is time = distance/speed.

Apply the numbers

Apply the given numbers of distance and speed to the rearranged formula: time = \(3.84 \times 10^{8}\)/\(3.0 \times 10^{8}\).

Calculate the time

Perform the division to obtain the time: time = 1.28 seconds. The calculation reveals that it takes approximately 1.28 seconds for a radio wave to travel from Houston to the surface of the Moon.

Key concepts

Speed of Light

Understanding the speed of light is crucial when discussing radio waves, as they both share the same remarkable velocity. The speed of light is a constant in physics, denoted as approximately - \(3.0 \times 10^{8}\) meters per second. This incredible speed allows light to travel from the Sun to the Earth in just about 8 minutes.

This speed represents the maximum velocity at which information or matter can travel in the universe. Hence, it provides a fundamental limit not only in physics experiments but also in practical technologies such as communications and astronomy.

When you think about radio waves, you can imagine them as a series of electromagnetic waves generated by the oscillation of electrons. This energy propagates at the speed of light through various media, including air and even the vacuum of space.

Distance Calculation

Calculating distance is often the first step in solving for time when using the speed of an object. In our example, the distance between the Earth and the Moon is - \(3.84 \times 10^{8}\) meters. This measurement represents the path that the radio waves must travel from mission control in Houston to the astronauts on the Moon.

To compute this, we usually need a starting and ending point and often rely on known values for constant measurements like the distance to the Moon. Thanks to years of astronomical data, we can accurately measure this distance with tools such as radar and laser ranging.

When tackling exercises involving distance, always review whether you are given a straight path measurement or whether the path includes detours or obstacles. This simplifies understanding what exactly you'll be calculating during a problem like sending a communication signal into space.

Time Calculation

Time calculation can seem tricky at first, but when you break it down, it's simply about organizing known values into an easy-to-use formula. In our exercise, the key formula used is:- \[ \text{time} = \frac{\text{distance}}{\text{speed}} \]This equation helps you find out how long radio waves take to travel the known distance to the Moon at the speed of light.

By substituting the distance - \(3.84 \times 10^{8}\) meters and the speed of light - \(3.0 \times 10^{8}\) meters per second, you perform a simple division operation to discover that radio waves will take roughly 1.28 seconds.

Breaking down calculations into this straightforward system helps you solve many science problems. It's about clearly identifying known values and inserting them into the correct formulas. With this same approach, you can tackle a variety of speed, distance, and time challenges, turning complex-looking questions into solvable equations.