# Looking for some help on a maths c assignment

• Aug 6th 2012, 05:20 AM
machito
Looking for some help on a maths c assignment
Falling objects experience two forces as they fall – weight (Earth’s attraction of the object) and air resistance.Air resistance is a complicated phenomenon that is generally ignored at the high school level due to the difficulty with the mathematics and the case specific nature. In general, air resistance is stated as being proportional to the square of the velocity using the following relationship.F_DRAG=kv^2The constant ‘k’ is related to the density of the fluid (in this case air), the cross-sectional area facing the resistance and a fudge factor related to the shape of the cross-sectional area.According to Newton’s Second Law, F(net) = ma, an object will experience an acceleration (speeding up/slowing down) if there is a net (or resultant) force acting on that object. When the net force is zero, the acceleration is zero and the object is then moving at a constant velocity. The net force is the sum of all of the forces acting on the object. In this case:F_net=F_g-F_DRAG=mg-kv^2So consider a skydiver jumping out of a perfectly serviceable aircraft, as he falls, his velocity increases and hence the air resistance will also increase. This will continue until the air resistance and the attraction of the Earth become equal and the net force on the skydiver will be zero and the skydiver no longer accelerates – this is terminal velocity.Consider an 80kg skydiver, his ‘jump’ will then have two sections free-fall (parachute closed) and slow descent (parachute open). Given that a=dv/dt and F_net=ma, use differential equations to find the equations for v(t) that describe both sections of the fall. (Assume initial (downward) velocity is 0 m/s and the chute is deployed when the skydiver reaches free-fall terminal velocity.) Draw a graph showing both sections of the fall showing all significant points. Calculate the terminal velocity for parachute open – does changing when you open the parachute (ie at a lower fall velocity) affect this terminal velocity. Justify. At what altitude should the skydiver exit the plane – fully justify your report