TBR Review Physics Chapter 1 Ex. 1b

[Nitabeat92]

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I just started going over Physics review with TBR Physics and I had a question about one of their examples.
Example 1.1b
How fast is a car traveling in miles per hour if it has a speed of 0.02906 km/s? (1
mile = 1609.38 m)
A. 0.018 miles/hr
B. 1.1 miles/ hr
C. 65 miles/hr
D. 780 miles/hr
Solution
Using the Test Tips from Example 1.1, you will find the order of magnitude to be
10^1 and the remaining numbers (i.e., 29.06 x 3.6/1.60938) to be equal to some
number between one and ten. The order of magnitude of the actual answer must
be 10^1.
The best answer is choice C.
My question is how are the remaining numbers equal to some number btwn 1 and 10 ?

Thank you!

 

[NextStepTutor_3]

Interesting question - as you've written the "remaining numbers," you're completely right - they aren't between one and ten, they work out to something around 65. In other words, something is incorrect about this solution. Since these "remaining numbers" fall somewhere between 10 and 100, the order of magnitude should actually be listed as 10^0 (which would give us 65 * 10^0, or the right answer).

However, it's very possible that, when the solution mentioned the order of magnitude being 10^1, they meant that 29.06 is equal to 2.906 x 10^1. This way, our "remaining numbers" would turn into (2.906 x 3.6) / (1.60938). That expression is absolutely between 1 and 10!

Does this make sense? This is a good question, and it seems like you know how to do it and were just wondering about that inaccuracy with the "between 1 and 10" business. But I can also multiply it out if anyone else is also confused!

 

[shefv]

I know this is a simple conversion problem but for some reason I keep getting the wrong answer - how did you solve it?

(0.02906 km/s) x (1 mi/0.160938 km) x (3600 s / hr)

approx. 3600/8 ?

What am I doing wrong?

 

[EParker37]

I know this is a simple conversion problem but for some reason I keep getting the wrong answer - how did you solve it?

(0.02906 km/s) x (1 mi/0.160938 km) x (3600 s / hr)

approx. 3600/8 ?

What am I doing wrong?

1609.38 m does not = .160938 km, it would be 1.60938km.

Also, the way to solve this isn't to actually do the conversion. We can immediately eliminate A/D since the numbers are too small and large. So we are left with B/C

We can estimate the answer now since those values have an order of magnitude of difference.
.029km/s approx = .030 km/s
3600s/hr can be rounded down to 3000
.030 * 3 = .090 * 1000 = 90km/hr
We know that 1mi = 1.6 km, thus, the only answer that makes any sense in comparison is answer choice C.