Conversion Problem?

Question

The 100.0m dash record is 9.780 s. What's the avrg speed in ft/s & mi/h. Please explain your process so I can learn how to do this.
Thanks

Answer 1

Simple
We have:
1000 meters in 1 kilometer
3.28 feet in 1 meter
5280 feet in 1 mile

So
v=s/t=100/9.78=10.22 m/s
or
v=(10.22meter/sec)x(3.28feet/meter)=
= 33.54 feet/sec
or
v=33.54 feet/sec ( (1/5280)miles/feet )
v= 0.00635miles/sec (3600 sec/hour)=
v=22.87 miles/hour

I hope it helps

Answer 2

use unit factor method, it is also called Demensional Analysis.
The idea goes like this: create several fractions next to each other and multiply. Each fraction, except for the starting one, has the value = to one. The fractions are created from equalitiis. Example 12 in = 1 ft, can be made into a unit factor. 12in / 1 ft or 1 ft / 12 in either fraction has the value of one. In your problem several unit factors will be used.

2.54 cm = 1 in
100 cm = 1 m
12 in = 1 ft
5280 ft = 1 mile
60 sec = 1 min
60 min = 1 H

problem #1 convert to ft per second.

(100.0 m / 9.780 s ) ( 100 cm / 1 m) (1 in / 2.54 cm) (1 ft / 12 in)

= 33.53 ft/ s

problem # 2 convert to miles per hour

(33.53 ft / s) (1 mile / 5280 ft) (60 s / 1 min) ( 60 min / 1 H) =

22.86 miles / Hour

Answer 3

1. organize the information that you have
a. 100.0 meters is the distance
b. 9.780 s is the time

Understand the question - you are asked for speed with specific units.

Speed = distance/time (so already you have 100.0 m divided by 9.780 s which is 10.2 meters/second.)

First you have to know your conversions.
a. how many meters in a foot (how many feet in a meter)
b. how many meters in a mile, (how many miles in a meter)

It does not matter which conversions you use, but in order to do it and get the correct answer, you MUST remember the units.

c. There are of course 60 seconds/min and 60 min/hr.

A. speed in ft/s

There are 3.28 feet per meter (you can find in textbook) so from the above average speed of 10.2 meters/second multiply by 3.28 feet per meter

10.2 m/s X 3.28 ft/m = 33.456 ft/s (because the meters cancel out)
Round off to 33.5 ft/s .....this is the first answer.

B. Second part of question. - is a two part answer (I do not suggest using answer A to do the second part - because what if you made a mistake???)

One meter is 0.0006213 miles.

10.2 meters/second X 0.0006213 miles/meter = 0.006337 mile/second

Now change this to hours - there are 60 seconds in one minute and 60 minutes in one hour
1 s X 60 s/min x 60 min/h = 3600 s/h.

0.006337 miles/second X 3600 seconds/hour = 22.81 miles/ hour (the second units cancel out) ..... second answer

Therefore, 10.2 m/s = 33.5 ft/s = 22.8 mi/h.

Finished.

Answer 4

all we have to do is dimensional analysis. if we know all our conversion factors, then just by multiplying by simple ratios we can solve our problem

first we start with what we know (sometimes this is called a basis). in this case we start with 100/9.780 seconds or 10.223 m/s.
(10.225 m/s)(100 cm/1m)(1in/2.54cm)(1 ft/12in)

we can see how our units cancel just to leave ft/s. we get about 33.55 ft/s

even though it would be easier to start with ft/s when we convert to mi/h, we might have made a mistake so we still want to start with m/s
(10.225m/s)(.000621 mi/m)(3600 s/hr)

this gives us about 22.9 mi/hr

Answer 5

100m/9.78s=10.225meters/second
=10.225m/s

Because second remains same for the speed unit you are looking for, you need to know conversion from meters to feet
Suppose there are "x" feet in a meter, 10.225 * x ft/s

In order to to convert from ft/s to m/h , you need to convert ft to miles and seconds to hr. As there are 5280 ft in a mile , so"x" ft equal to "x"/5280 miles, 1 sec equals to 1/3600 hrs
=3600*10.225* x /5280 m/h
=6.972 *x m/h
as there are 3.28 ft in a meter, so x=3.28
10.225*3.28=33.538ft/s
or 6.972*3.28=22.868m/h