a) Consider a coordinate system where the x and y coordinates are both zero when the ball passes through the pivot and lands on the top of the table at that same level (y = 0). The ball then starts at y = 0 and reaches y = 0 again when landing on the table. The range R will simply be the x coordinate where it hits. Draw your theoretical quantitative predictions for the range R as a function of the initial angle α of 15◦ , 30◦ , 45◦ , 60◦ , 75◦ on the following graph. Make sure the points are correct relative to each other. Assume there is no air resistance.
Enter your predictions on the graph assuming the range at 45○ is 9 (enter that point as well). That is the point with coordinates (45,9) is your reference point for the range at 45○and you are required to calculate the missing coordinates for the points (15, range at 15○ w.r.t. range at 45○), (30, range at 30○ w.r.t. range at 45○), etc.
b) Draw your quantitative predictions for the trajectory on the following graph for 15◦ , 30◦ , 45◦ , 60◦ , 75◦ . (These will be lines of motion.) Assume there is no air resistance.
a) Consider a coordinate system where the x and y coordinates are both zero when the...
3. Polar Coordinates. (a) Given a rectangular coordinate point (x, y), how do you compute the equivalent polar coordinates: (r, 0)? (b) Given a polar coordinate (r, o), how do you compute the equivalent rectangular coordinate: (x, y)? (c) Consider the drawing in Figure 1. Compute the coordinate of each small circle. (d) What if the circle is centered at the point (cx, cy) (and not the origin). How does the formula change?
Use a polar coordinate system to plot the point with the given polar coordinates. Then find another representation (r,θ) of this point in which: Use a polar coordinate system to plot the point with the given polar coordinates. Then find another representation (r,0) of this point in which: (b) r< 0,0 <θ<2x. Choose the correct graph below. O A O B O C. O D. ピ -5 (a) What are the coordinates of the point for which r > 0,...
Under the standard (x, y)-coordinate system, a grid of points with integer coordinates is given in the picture below. Here, the bottom-left point is the origin (0, 0) and the topright point has coordinate (6, 3). The coordinates of the remaining points can easily be computed accordingly. 2 During the 74th Hunger Game, Katniss and Peeta are separated inside a grid maze. Katniss is currently at the point (0, 0) and Peeta is (badly injured) at the point (x, y)...
Consider a rectangular coordinate system with origin at the center of the earth z-axis through the North Pole, and -axis through the prime-meridian. Find the rectangular coordinates of London, England (51°32'N, 0°5'W). A minute is 1/60°. Assume the earth is a sphere of radius R 6367 km. London has coordinates -914.56,4341.06,4567) Usage: To enter a point, for example (x, y, z), type "(x, y, z)" Consider a rectangular coordinate system with origin at the center of the earth z-axis through...
2. A baseball thrown from the outfield, a golf ball, or a thrown football, all will follow a trajectory (path) that has horizontal as well as vertical displacement components. If we neglect the air friction on the ball, the path will be a perfect parabolic trajectory. The equations for the displacement of the ball are: Take gravity g as 9.81 meters per second, and the initial velocity, Vo, equal to 35 meters/second. Use Excel to show the ball trajectory for...
inorderDraw(): This function assigns x coordinates to nodes so that each node gets a distinct x-coordinate, and each node receives an x-coordinate between that of its two children. _____________________________________ package comp2402a4; import java.util.Random; public class GeometricTree extends BinaryTree { public GeometricTree() { super (new GeometricTreeNode()); } /** * Set the x and y-coordinates of each node such that it is between the * x-coordinate of its two children, no two nodes have...
3. A ball of mass m=0.5kg is thrown at 1 meter above the ground (meaning X; = 0, Y; = 1m) and with an initial velocity of Vo=600 m/s along degree (with respect to the horizontal X-axis). a) Starting from Newton's second law, find V (t), Vy(t), X(t), and Y(t). b) From a), find the range R and the maximum height Y max the ball can reach. c) i) Plot the trajectories of the ball using the results in a)...
Write a Java program which uses the LWJGL library to draw a window of 640x480 (with a black background). The coordinate system should be centered in this window. Your program will read a file titled coordinates.txt and draw the corresponding filled polygon in this window using the scanline polygon fill algorithm. Each specified polygon should be filled in the color specified in the text file and then undergo the transformations specified in the input file before being drawn on the...
Please find the following for the required problem attached : 1- Motion diagram with coordinate axis 2- positive Vs. time graph 3- velocity Vs. time graph (well labeled) 4- find the total distance and time for the entire play and explain how this was determined (In a clear handwriting please). 5- Show mathematical work with the proper equations to calculate anything and everything of interest including how long was the entire play. Thanks Quarterback Bill throws the ball to the...
BOX 5.1 The Polar Coordinate Basis Consider ordinary polar coordinates r and 0 (see figure 5.3). Note that the distance between two points with the same r coordinate but separated by an infinitesimal step do in 0 is r do (by the definition of angle). So there are (at least) two ways to define a basis vector for the direction (which we define to be tangent to the r = constant curve): (1) we could define a basis vector es...