Answer Happy

1.1. The range of the projectile is the distance from the origin to the point of impact on horizontal ground. It is given by R = v, cos(6.). To estimate the range, your trajectory plots should be altered to have the horizontal distance on the x-axis and the altitude on the y-axis. This representation will clearly show the path of the projectile launched with a certain initial angle. This means you will have to plot y vs. X. Observing the formula for the projectile's range, we see that to increase the range we will have to adjust the launching angle. Use the following adjusted angles to create two more trajectory plots (y vs. x), one for each angle, and determine which launching angle results in a greater range: 51 05 = 4.17 – 0.255) radians and 12 (511 0% = 4.17 – 0.425) radians 12 The time vectors for these angles should be defined as t = 0:0.1:9 and t = 0:0.1:8 respectively.
1.3. Your task is to graph algorithms with the following big-O characteristics: Algorithm #1: O(n Inn) Algorithm #2:0(/n) Algorithm #3: O(Inn) Note: The In function in Matlab is given by log(). Print both the linear and logarithmic plots, using a domain from n=1 to n = 500 to observe the considerable improvement in readability that a logarithmic scale for the y-axis will provide. The logarithmic scale is very useful when attempting to compare values that are orders of magnitude apart on the same graph. Do not use a grid for the logarithmic scale.
1.2. a) Using the plot command for multiple plots, plot y = tan-(x) and y = cot-'(x) on the same graph for values of x defined by x = ITI. 2' 30'2 b) Using the plot command for a single plot and the hold commands, plot y = tan-'(x) and y = cot-'(x) on the same graph for values of x defined by x c) Using the ezplot command, plot y = sin(9nx), for values of x such that 0 sxs 21. пп л 2302