Solve the following problems with Maple, then compare your answers to my solutions.
On most computers you may do the following to avoid any flipping back and forth between a problem statement and your Maple worksheet. To the right of the undo and redo buttons in the worksheet toolbar is a set of three buttons for controlling the Maple prompt and input modes. Click the new execution group button ( [> ) to create a new Maple prompt and execution group below the execution group in which the cursor currently rests. Next click the middle button of the set ( T ) to put Maple into the text input mode. Now copy and paste the problem statement from your browser window into your Maple worksheet at the cursor in the newly created text input mode execution group. Click the new execution group button once more to create another Maple command prompt.
In your solutions to the problems, where appropriate, assume that the acceleration due to gravity is 10 m/s^2 and that there is no air resistance.
(1) It takes 1/30 s to produce a complete image on a television screen. An electron beam travels across the screen 525 in this time, positioning itself a little lower on the screen with each pass. (a) How fast does the electron beam travel across a screen with a width of .5 m? (b) If the electron beam starts at the upper left hand corner of the screen and ends at the lower right hand corner of the screen, and the television is square, what is the magnitude of its average velocity?
(2) In order to make a long journey a spaceship must travel as fast as possible. Relativity and engineering technology limit its maximum speed to about one-tenth the speed of light (the speed of light is 3x10^8 m/s). To avoid psychological stress on the ship's occupants, the ship can accelerate at only 10 m/s^2. (a) How many years does it take the ship to reach its maximum speed? (b) How far does it travel in that time? Use the plotting technique described in Kinematics 1 to plot the position vs. time graph of the spaceship (use seconds for time).
(3) A jealous lover stands at the edge of a 50 m tall building holding a tomato. If a man flirting with the lover's girlfriend below walks at 1 m/s towards the building, and the man is the tomato's target, at what distance should he be from the building when the jealous lover drops the tomato ? Assume either that the flirt has no height, or that the tomato will hit his spiffy new shoes.
(4) A bat flying towards a wall sends out a sound wave at a distance of 2 m from the wall. The sound wave travels at 330 m/s. If the bat is flying at 20 m/s, how far will it travel in the time it takes for the sound wave to hit the wall and return to the bat?
(5) A stampeding herd of bulls moves at a speed of 7 m/s. A boy standing at rest 20 m in front of the bulls starts accelerating at 3 m/s^2. Will the boy make it, i.e. will he not be trampled? Use the plotting technique described in Kinematics 1 to plot the time vs. position graphs of the boy and the bulls on the same set of axes. Plotting hint: You may select and place a single variable expression that is not an equation into a live 2D plot fame. The variable displays along the horizontal axis and the value of the expression displays along the vertical axis. I'm asking you to do something here that I did not explain in the example problem, but the hint and a little experimentation on your part should enable you do do it.
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