Solve the following problems with Maple, then compare your answers to my solutions. See Kinematics 1 Problem Set for instructions on how to avoid switching back and forth between a problem statement in your browser window and your Maple worksheet.
In all of these problems assume that the acceleration due to gravity is 10 m/s^2 and that there is no air resistance.
(1) Robin Hood wants to split an arrow already lodged horizontally into the bull's-eye of a target 40 m away. (a) If he aims directly at the arrow in the target, by how much will he miss if the arrow in his bow leaves the bow at 140 m/s? (b) Create a parametric plot of the flight of the arrow. Use the plot function, label the axes, and a give it a title. Do not use the scaling = constrained parameter.
(2) Danger Dana wants to jump the Grand Canyon of the Snake River by being shot from a cannon. In order to spend more time in the air waving at the crowd, she wants to be launched at a 60 degree angle above the horizontal. (a) If the canyon is 520 m wide, what must her launch speed be for her to just reach the other side? Hints: Maple provides all the trigonometric functions, including sin and cos. All arguments to Maple trig functions must be in radians, and 1 radian = 180/ Pi degrees. (b) Create a parametric plot of the x and y-positions of Danger Dana. Use the plot function, label the axes, and give it constrained scaling and a title.
(3) At what angle and at what initial speed should a football punter kick a football if the punter wants it to land 50 m away and stay in the air 4 s. Assume the ball leaves the punter's foot at a elevation of 1 m, and that the horizontal distance is measured from this point, also. Create a parametric plot of the football's flight. Use the plot function, label the axes, and give it constrained scaling and a title.
(4) Babe Ruth hits a ball that leaves his bat with a speed of 33.55 m/s at an angle of 37 degrees above the horizontal. The ball is 1.22 m above the ground and 106.75 m from the outfield fence. The outfield fence is 3.05 m high. (a) At what times after being hit will the ball reach the height of the fence? (b) How far along the x-axis from the batter will the ball be at these times? (c) Has Babe hit a home run? (d) Create a parametric plot of the ball's flight path between the points that it is 3.05 m above the ground. Use the plot function, label the axes, and give it constrained scaling and a title.
Kinematics 2 Top Newton's 2nd Law of Motion
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