Question

physical therapists are often contracted to certify that firefighters are able to do task that model what they must be able to do when firefighting. in one task, a firefighter must thrust a 20 pound weight horizontally so that it lands at least 18 feet away. if the firefighter has a shoulder height of 4.5 feet, what is the minimum speed in feet/s at which the weight must be thrown?

Answer 1

Given:

physical therapists are often contracted to certify that firefighters are able to do task that model what they must be able to do when firefighting. in one task, a firefighter must thrust a 20 pound weight horizontally so that it lands at least 18 feet away. if the firefighter has a shoulder height of 4.5 feet, what is the minimum speed in feet/s at which the weight must be thrown?

  

The differential equation of the 20lb weight in the y direction is :

   with   and   . Integrate with respect to t , and we get :

  . Integrate with respect to t again , and we get:

   (1)

In the x direction , the differential equation for the weight is :

   with   and   . Integrate with respect to t , and we get :

  . Integrate again with respect to t , and we get :

   (2)

From equation (1) , we can solve for the time it takes for the 20lb weight to drop from shoulder height y(0)=4.5feet to y = 0 feet :

===>

===>

===>

   . Now , substitute this value into equation (2) because the weight must travel 18feet horizontally in the time it takes to drop from shoulder height to the ground :

   ===>

   --- SOLUTION .