You are watching: A ball is kicked with an initial velocity of 16 m/s in the horizontal direction
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This is university Physics Answers v Shaun Dychko. A sphere is kicked so that it has an early stage x-component the its velocity of 16 meter per 2nd and a y-component at first upwards of 12 meters every second. And component A asks us, at what speed does the ball hit the ground? therefore we require to uncover the resultant of its two materials after it hits the ground over right here somewhere. So we’ll attend to each component separately, we"ll think about the x-component first. Then we"re going to use this formula; we’ll say that the last velocity along any type of dimension be it x or y, amounts to initial velocity, plus acceleration, time time. But in the x-direction there"s no acceleration due to the fact that gravity acts just vertically, and so we put zero in for A. And so the moment doesn"t yes, really matter and we end up with the initial x-velocity is the last x-velocity. In other words the x-component that the velocity that the ball doesn"t readjust as it"s moving. And so it"s going to it is in 16 meters per second when it access time the ground. In the y-direction, we"ll use this formula; which has actually the last velocity squared equates to initial velocity squared, plus two times acceleration, times displacement. And also we recognize the displacement is zero once it returns ago to its early stage height, this is the vertical displacement. Once it hits the ground, vertical displacement is zero. So this entire term is zero and also we"re left with the final velocity in the y-direction squared, amounts to initial velocity in the y-direction squared. And also so us take the square source of both sides. And also when you carry out that, friend don"t understand whether the left side is going to be the confident or the negative square source of the appropriate side. Therefore we have the right to take our pick and also we’ll choose an unfavorable because we deserve to see indigenous this, from our understanding of the physics below that the round is walk to it is in going in the bottom direction like this. And so is walking to have a negatively directed y-component that its velocity here and so we pick the negative. Therefore the last y-velocity climate is an adverse 12 meters every second. Therefore the final velocity in full is walking to it is in the Pythagorean amount of these two components. So us take the square root of the x-component squared, add to the y-component squared; so we have actually square root of 16 meters per second square, plus an unfavorable 12 meters per second squared. Providing us 20 meters per second, is the final velocity when the sphere hits the ground. Part B asks, for just how long walk the ball remain in the air? We’ll use this formula to answer the question since we know whatever in here other than for t. We know the final y-velocity, the early stage y-velocity and also the acceleration. So fine subtract the early y-component native both sides and also then division both sides by A. And we end up through this formula below after switching the sides around, therefore we have t equates to the final velocity in the y-direction, minus the early stage velocity in the y-direction, separated by the vertical acceleration. Therefore that"s an adverse 12 meters per 2nd as the last y-velocity, that"s what we discovered here. And also then subtract from that the early y-velocity i beg your pardon is hopeful 12 meters every second, and also divide that by the acceleration, i beg your pardon is command downwards in ~ 9.8 meters second squared. And that gives 2.4 secs as the lot of time that will invest in the air. Component C asks, what is the maximum height attained through the ball? therefore we need to understand that the y-velocity will certainly be zero when the round reaches its best height. And so learning that, we deserve to use this formula to figure out what that maximum height will be. Therefore in the y-direction, we have the right to say that the final velocity squared, which is zero, equates to the early stage y-velocity squared, plus two times vertical acceleration, times vertical displacement. Therefore we"ll settle for d by subtracting the early stage y squared from both sides. And also then division both sides by 2a and also we end up v the maximum height or the vertical displacement in various other words, is negative the early stage y squared over two, time acceleration. So that"s an unfavorable of 12 meters per 2nd squared, divided by two, times an adverse 9.8 meters per 2nd squared, which is 7.3 meter maximum height.