Question

Just set up do not need to evaluate an IVP whose solution will give the velocity of the body and his sled t seconds after he starts down the hill described by the following conditions. Remove all the trigonometric and inverse trigonometric expressions from your final differential equation. A boy and his sled weigh W pounds. Starting from rest at t=0, the boy and his sled slide down a snow -covered hill whose slope is 2/5. As he slides down the hill on his sled, the boy and his sled are acted upon by air resistance (in lbs) that is numerically equal to three times his velocity (in ft/sec). The coefficient of sliding friction of the runners on the sled agains the snow-covered hill is 1/25.

Answer 1

The slope of the hill is given by

The force of gravity acting parallel to the slope is (taking positive sign for the direction of motion)

there are two forces acting against that: the force due to friction:

and the force due to air resistance which is given proportional to velocity:

Here the weight W relates to the mass m and acceleration due to gravity g (in relevant units of ft s^-2) as

These three forces must superpose to give the rate of change of momentum of the boy and sled system:

we have

Hence the final differential equation is

with initial condition