In-class exercise 1

The adventures of Betaman

A priceless water balloon of mass 25 kg is thrown from a helicopter by the evil Snydely Whiplash.  Our tiny flying superhero Betaman tries to save it.  By the time Betaman catches up with the balloon, it is 120 m from the ground travelling downward at 5 m/s.  The balloon feels an air drag force of magnitude 0.3(v^2) in newtons (v is the instantaneous velocity in m/s of the balloon), and Betaman exerts an upward force that increases in time as (Subscript[F, B])=10 (t^2) newtons, where t is measured from the instant he catches up with the balloon.  The balloon will break if it hits the ground with a speed greater than 2.3 m/s.  Does Betaman save the balloon?  If so, how close did the balloon come to breaking?  Use g=9.8.

Numerical projectile problem

Remove["Global`*"]

Here, we want to determine the time of flight for a projectile launched straight up into the air experiencing quadratic drag.  We want the time of flight as a function of initial speed, assuming that all other relevant parameters are given.

Start by finding the time of flight for initial speed of 5 m/s.  Assume a drag force of magnitude of 0.1(v^2).

Fd=
eqy=

m=1;k=0.1;g=9.8;

v=5

sol=NDSolve[{},y[t],{t,0,10}]

Y[t_]=

FindRoot[]

v=.
t=.

Now define a function that returns the time of flight.

m=1;k=0.1;g=9.8;
Fd=
eqy=

TimeInAir[v_]:=(
)

TimeInAir[5]

Plot[TimeInAir[v],{v,0.1,50}]

Now get a list of times of by using Table[] to construct a list of ordered pairs (v, time of flight).  Choose values of v from 1 to 50 in steps of 0.5.  Plot the result.

Ttab=Table[FILL_IN_WITH_CODE,{v,1,50,0.5}]

ListPlot[Ttab]