[amp_mcq option1=”0.5 m\/sec” option2=”1.5 m\/sec” option3=”2.5 m\/sec” option4=”3.5 m\/sec” correct=”option1″]<\/p>\n
The correct answer is $\\boxed{\\text{B) 1.5 m\/sec}}$.<\/p>\n
The coefficient of restitution is a measure of how much energy is lost in an elastic collision. A value of 0.5 indicates that half of the energy is lost, while a value of 1 indicates that no energy is lost.<\/p>\n
In this case, the ball is moving with a velocity of 5 m\/sec and impinges a fixed plane at an angle of 45\u00c2\u00b0. The direction after impact is equally inclined to the line of impact. This means that the ball will bounce off the plane at an angle of 45\u00c2\u00b0, and its velocity after impact will be equal to its velocity before impact, but in the opposite direction.<\/p>\n
The coefficient of restitution is given by the equation $e = \\frac{v_f – v_i}{v_i – v_f}$, where $v_f$ is the final velocity, $v_i$ is the initial velocity, and $e$ is the coefficient of restitution.<\/p>\n
In this case, we know that $v_i = 5$ m\/sec, $v_f = -5$ m\/sec, and $e = 0.5$. Substituting these values into the equation, we get $0.5 = \\frac{-5 – 5}{5 – (-5)}$. Solving for $v_f$, we get $v_f = 1.5$ m\/sec.<\/p>\n
Therefore, the velocity of the ball after impact is $\\boxed{\\text{1.5 m\/sec}}$.<\/p>\n
Option A is incorrect because the velocity of the ball after impact cannot be 0.5 m\/sec. The ball is moving with a velocity of 5 m\/sec before impact, and the coefficient of restitution is 0.5. This means that the ball will bounce off the plane at an angle of 45\u00c2\u00b0, and its velocity after impact will be equal to its velocity before impact, but in the opposite direction. The final velocity cannot be less than the initial velocity, so option A is incorrect.<\/p>\n
Option B is correct because the velocity of the ball after impact is 1.5 m\/sec. The ball is moving with a velocity of 5 m\/sec before impact, and the coefficient of restitution is 0.5. This means that the ball will bounce off the plane at an angle of 45\u00c2\u00b0, and its velocity after impact will be equal to its velocity before impact, but in the opposite direction. The final velocity cannot be less than the initial velocity, so option A is incorrect. The final velocity cannot be greater than the initial velocity, so option C is incorrect. Option B is the only option that is consistent with the given information.<\/p>\n
Option C is incorrect because the velocity of the ball after impact cannot be 2.5 m\/sec. The ball is moving with a velocity of 5 m\/sec before impact, and the coefficient of restitution is 0.5. This means that the ball will bounce off the plane at an angle of 45\u00c2\u00b0, and its velocity after impact will be equal to its velocity before impact, but in the opposite direction. The final velocity cannot be greater than the initial velocity, so option C is incorrect.<\/p>\n
Option D is incorrect because the velocity of the ball after impact cannot be 3.5 m\/sec. The ball is moving with a velocity of 5 m\/sec before impact, and the coefficient of restitution is 0.5. This means that the ball will bounce off the plane at an angle of 45\u00c2\u00b0, and its velocity after impact will be equal to its velocity before impact, but in the opposite direction. The final velocity cannot be greater than the initial velocity, so option D is incorrect.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”0.5 m\/sec” option2=”1.5 m\/sec” option3=”2.5 m\/sec” option4=”3.5 m\/sec” 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-6763","post","type-post","status-publish","format-standard","hentry","category-applied-mechanics-and-graphic-statics","no-featured-image-padding"],"yoast_head":"\n