Question

If the true velocity of a rocket is 711 m/s, which of the following measurements taken on that velocity would be the most accurate?
answers:
v = 502.8 m/s

v= 502.8 m/s

v= 681.7 m/s

v= 707.9 m/s

Answer 1

To determine which measurement is the most accurate compared to the true velocity of the rocket (711 m/s), we need to calculate the absolute differences between the true velocity and each of the provided measurements.

1. For \(v = 502.8\) m/s:
\[
|711 - 502.8| = 208.2 \text{ m/s}
\]

2. For \(v = 502.8\) m/s (duplicate):
\[
|711 - 502.8| = 208.2 \text{ m/s}
\]

3. For \(v = 681.7\) m/s:
\[
|711 - 681.7| = 29.3 \text{ m/s}
\]

4. For \(v = 707.9\) m/s:
\[
|711 - 707.9| = 3.1 \text{ m/s}
\]

Now we compare the absolute differences:

- \(v = 502.8\) m/s: 208.2 m/s
- \(v = 502.8\) m/s: 208.2 m/s
- \(v = 681.7\) m/s: 29.3 m/s
- \(v = 707.9\) m/s: 3.1 m/s

The smallest difference is for \(v = 707.9\) m/s, which is 3.1 m/s away from the true velocity of 711 m/s.

Thus, the most accurate measurement is **v = 707.9 m/s**.