Question

How do you convert 42 miles per hour to feet per second?

Answer 1

Hint:
There are 5280 feet in a mile and 3600 seconds in an hour (60 minutes x 60 seconds). So, here we will convert both mile and hour to feet and second to solve this problem. We can also convert miles to yards and then yards to feet to find the solution.

Complete step by step solution:
The given problem statement is to convert 42 miles per hour to feet per second.
For the above problem, we know that there are 5,280 feet in a mile and 3600 seconds in an hour. To convert 42 miles per hour to feet per second, we have to first convert miles to feet.
 $\Rightarrow 5280ft=1mi$
Rewriting the equation, we get,
$\Rightarrow 1mi=5280ft$
Dividing both sides with 1mi, we get,
$\Rightarrow {\displaystyle \frac{1mi}{1mi}}={\displaystyle \frac{5280ft}{1mi}}$
Now simplifying, we get,
 $\Rightarrow 1={\displaystyle \frac{5280ft}{1mi}}$
Now we will multiply 42 miles per hour with ${\displaystyle \frac{5280ft}{1mi}}$, we get,
 $={\displaystyle \frac{42mi}{hr}}\times {\displaystyle \frac{5280ft}{1mi}}$
We will cancel the miles as they are cross multiplied, we get,
 $$={\displaystyle \frac{42}{hr}}\times {\displaystyle \frac{5280ft}{1}}$$
After multiplying 42 with 5280 we will get,
 $={\displaystyle \frac{221760ft}{1hr}}$
Next, we have to convert 1 hour to seconds. We know that $1hour=3600\sec$
Now, replace 1 hr with 3600sec in ${\displaystyle \frac{221760ft}{1hr}}$, we get
 $={\displaystyle \frac{221760ft}{3600\sec }}$
After dividing the numerator and denominator we will get,
$={\displaystyle \frac{61.6ft}{\sec }}$

So, 42 miles per hour is equal to 61.6 feet per second.

Additional Information:
Whenever we are doing the conversion with the length that means we are converting from one unit to another. We need to find the correct relationship between the two units and depending on that we will multiply or divide.
For example:
We need to convert 3km to m. The relationship between the two units is $1km=1000m$. So, to convert 3 km to m we need to multiply 3 with 1000 that is
$\Rightarrow 3km=3\times 1000=3000m$

Note:
We can solve this problem with an alternative method.
 $\Rightarrow miles\to yards\to feet$
 $\Rightarrow miles\times 1760\to yards\times 3\to feet$
Converting hour to seconds:
 $\Rightarrow 1hour\times 60\to 60min\times 60\to 3600\sec$
Now, we will first convert miles to yards then feet and hour to seconds
 $\Rightarrow {\displaystyle \frac{42miles}{1hour}}={\displaystyle \frac{42\times 1760\times 3}{1\times 60\times 60}}{\displaystyle \frac{feet}{\sec }}$
After simplifying, the above equation, we get,
 $={\displaystyle \frac{308}{5}}$ feet per second
After dividing the numerator and denominator we will get,
 $=61.6$ feet per second
So, 42 miles per hour is equal to 61.6 feet per second.