[amp_mcq option1=”$$\\alpha = \\frac{\\pi }{4} – \\frac{\\beta }{2}$$” option2=”$$\\alpha = \\frac{\\pi }{2} + \\frac{\\beta }{2}$$” option3=”$$\\alpha = \\frac{\\beta }{2} – \\frac{\\pi }{2}$$” option4=”$$\\alpha = \\frac{\\pi }{4} – \\frac{\\beta }{4}$$ E. $$\\alpha = \\frac{\\pi }{2} – \\frac{\\beta }{2}$$” correct=”option1″]<\/p>\n
The correct answer is $\\boxed{\\alpha = \\frac{\\pi}{4} – \\frac{\\beta}{2}}$.<\/p>\n
The range of a projectile is the maximum horizontal distance that it travels. It is given by the formula<\/p>\n
$$R = \\frac{v_0^2 \\sin(2\\alpha)}{g}$$<\/p>\n
where $v_0$ is the initial velocity, $\\alpha$ is the angle of projection, and $g$ is the acceleration due to gravity.<\/p>\n
The maximum range occurs when $\\sin(2\\alpha) = 1$, which means that $\\alpha = \\frac{\\pi}{4} – \\frac{\\beta}{2}$, where $\\beta$ is any integer multiple of $\\pi$.<\/p>\n
The other options are incorrect because they do not result in a maximum range. For example, if $\\alpha = \\frac{\\pi}{2} + \\frac{\\beta}{2}$, then $\\sin(2\\alpha) = 0$, which means that there is no horizontal displacement.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”$$\\alpha = \\frac{\\pi }{4} – \\frac{\\beta }{2}$$” option2=”$$\\alpha = \\frac{\\pi }{2} + \\frac{\\beta }{2}$$” option3=”$$\\alpha = \\frac{\\beta }{2} – \\frac{\\pi }{2}$$” option4=”$$\\alpha = \\frac{\\pi }{4} – \\frac{\\beta }{4}$$ E. $$\\alpha = \\frac{\\pi }{2} – \\frac{\\beta }{2}$$” correct=”option1″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[645],"tags":[],"class_list":["post-6694","post","type-post","status-publish","format-standard","hentry","category-applied-mechanics-and-graphic-statics","no-featured-image-padding"],"yoast_head":"\n