P2820 Midterm 1 - February 10, 2011

Name:
Student number:

There are 2 questions, each worth 10 marks.
Note: Do not worry about axes labels for plots, but do answer questions with sentences when appropriate and include units (give numerical answers to three significant figures).

Q1 [10 marks]

Two vehicles, A and B, both start travelling from rest down a straight line at time t=0.  The velocity of vehicle A is given in the following expression

Remove["Global`*"]
(3 t +Sin[4t])*Exp[-3t/10] +(1-Exp[-3t/10])12

a)

Plot the velocity of vehicle A from 0 to 30s.

b)

Plot the acceleration of vehicle A from 0 to 30s

c)

What is the maximum speed attained by vehicle A and when is that speed reached?

d)

Determine and plot the displacement of vehicle A from 0 to 30 s.

e)

Vehicle B moves with a constant acceleration of 0.9 m (s^(-2)).  When does vehicle B overtake vehicle A and how far have the vehicles travelled by this time?

Q2

Tired of Snidely Whiplash’s criminal antics, the tiny Betaman throws him straight down into a deep swimming pool.  At t=0, Snidely enters the water at a speed of 4 m/s.  In addition to gravity (g=9.8 m (s^(-2))), Snidely feels a drag force with magnitude in newtons of 1.8(v^2), where v is Snidely’s instantaneous velocity, and a bouyant force of 1.1mg in magnitude, where m is Snidely’s mass of 89kg.  

(Note: you must take into consideration that the direction of the drag force changes as Snidely changes direction at the maximum depth.)

a)

Using a built-in ODE solver, find and then plot the position of Snidely, assuming that the surface of the water is at y=0.  (It is understood that parts of the trajectory with y > 0 are unphysical remnants of the force model that you might be using.)

b)

To what depth does Snidely descend, and at what time does he resurface?