Dimensional Analysis can be used to approximate the number of seconds a major league batter has to react to a pitch. In Major League Baseball, pitches are measured in miles per hour, but distances on the field are measured in feet. Suppose a pitcher throws a 90 mph football.. Use dimensional analysis to convert the speed, or rate, from miles per hour to feet per second. Show your work

Before we can attempt converting 90 mph to feet per second, it is necessary that we first determine the value of one mile in feet and one hour in seconds.

1 mile is equal to 5280

1 hour is equal to :

1 minute ------ 60seconds

60 minutes ------- ?

(60/1) × (60/1)

= 3600 seconds.

Therefore 1hour = 3600seconds.

Since 90 mph will be converted to feet per second, we can convert 90 miles to feet first.

1 mile --------- 5280 feet

90miles ------- ?feet

90/1 × 5280

= 475200

So, the pitcher threw a 475200 feet per hour football.

Now, since 3,600seconds make 1 hour, we now determine how many feet the ball can cover in 1 second since the speed of the ball is 475200 feet in 3600seconds:

475200 feet ------ 1 hour(3600 seconds)

? feet ------- 1 second

= (1/3600)×(475200/1)

= 132 feet

Therefore converting 90miles per hour will give 132 feet/second

Alternatively, we can calculate this way:

(miles/hour) × [feet(1 mile in feet)/seconds( 1 hour in seconds)]

= (90/1) × (5280/3600)

= 132feet/sec