A Math and Physics Snow Dance

With the unseasonably warm winter we’ve been having, many of us are wondering if we’ll get a snow storm at all before spring comes. In hopes of snow, here are some snow-related math problems. They even tie in with what we’re currently studying in physics, pre-calculus, and AP calculus (work and energy, logarithms and exponents, and applications of derivatives, respectively)!  See if you can try to solve the following:

1.    It takes a snow plow 60.0 seconds to push a 5460 kg pile of snow along a straight level road at a constant velocity of 16 m/s. If the plow exerts a force of 7600 N on the snow, how much work does it do? What is the kinetic energy of the snow pile as it is being moved?

 2.  A snow removal company developed a logarithmic mathematical model for the number of miles  s  of roads that can be cleared of snow per truck per hour based on h, the depth of the snow in inches:

Use this model to find how many miles of roads can be cleared by one truck in one hour when  h=10 inches.

3.   There is no snow on Janet’s driveway when snow begins to fall at midnight. From midnight to 9 A.M., snow accumulates on the driveway at a rate modeled by  

cubic feet per hour,

where t is measured in hours since midnight. Janet starts removing snow at 6 A.M. (t=6). The rate g(t), in cubic feet per hour, at which Janet removes snow from the driveway at time  hours after midnight is modeled by

Find the rate of change of the volume of snow on the driveway at 8 A.M.
*Don’t forget to put your calculator in radian mode when evaluating trigonometric functions!

Answers

1.  

   

2.      27.16 miles of road

3.     To find the rate of change of volume of snow on the driveway at 8 A.M., you must subtract the snow removal function g(t) from the snow accumulation function f(t).

cubic feet per hour.


Kathy Wann
Math and Science Instructor