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Pant BThe ball is caught by the centerfielder who, starting at a distance of 110 m from home plate; rung swralght toward home plate at a constant speed and makes th...

Question

Pant BThe ball is caught by the centerfielder who, starting at a distance of 110 m from home plate; rung swralght toward home plate at a constant speed and makes the catch at ground level. Find his speed Express your answer using two significant figuresAz$m/sSubmitRequestAnswel

Pant B The ball is caught by the centerfielder who, starting at a distance of 110 m from home plate; rung swralght toward home plate at a constant speed and makes the catch at ground level. Find his speed Express your answer using two significant figures Az$ m/s Submit RequestAnswel



Answers

A batter hits a fly ball which leaves the bat 0.90 $\mathrm{m}$ above the ground at an angle of $61^{\circ}$ with an initial speed of 28 $\mathrm{m} / \mathrm{s}$ heading toward centerfield. Ignore air resistance. (a) How far from home plate would the ball land if not caught? ( $b )$ The ball is caught by the centerfielder who, starting at a distance of 105 $\mathrm{m}$ from home plate, runs straight toward home plate at a constant speed and makes the catch at ground level. Find his speed.

So if eso if this baseball isn't caught, what's its horizontal displacement? And then, given that the baseball is caught, what is the speed of this outfield runner? So we can say the Fada? So the ball is launched at an angle of sixty one degrees. This is considered a fly ball. Hit it. This is very close toe. Be being straight vertical, so it's going to be very. It's going to reach a very high point in the air and so we can say why initial equals point nine meters. So it Ah, the baseball is hit at initial velocity of point nine zero meters and then it lands on the ground. Of course, So the wife final will simply be zero meters. We're taking the ground to be why final? And so the initial equals twenty eight meters per second. That is the a speed the velocity and with with with the ball is hit by the batter. So if you wanted to find the time in the air, we can say why final equals. Why initial plus v y initial teeth plus one half a subway t squared. We know that ace of y equals negative. You were choosing down to be negative so we can say and my final zeros, we can say zero equals point nine plus and then this will be twenty eight. Sign of sixty one degrees Times time minus four point nine t squared. This is a quadratic equation. So you confuse the sol function on your tea. I eighty three eighty four eighty five for eighty nine in order to solve for tea, and he's going to be equal to five point zero three four seconds. So in order to find a part a are they want they'LL tow accident Final horizontal displacement If it isn't caught, this is going to be VX initial t So this would simply be twenty eight co sign of sixty one degrees times five point zero three four seconds and this is giving us sixty eight point three meters now for Part B. They're asking us what's the average velocity of this runner. So if the ball is the football, if the ball is travelling sixty eight point three meters past the home plate and the runner is going to be one hundred and five meters, that means that the change in displacement of the runner is going to be one hundred and five meters from home plate and that minus sixty eight point three meters from home plate, because again Ah, the ball is traveling some of the distance for him in a way. So you can say that if he's running from one hundred five meters away from home plate and the ball travels six point sixty eight point three meters away from home plate, essentially the bad, the catcher simply has to run one hundred five meters minus sixty eight point three and then again, this will be the divided by the time of flight of the ball. So there be one o five minus sixty eight point three, divided by five point zero three four and this means that the average velocity of the of the outfield player is going to be seven point two eight meters per second. So he'LL have to run seven point two eight meters per second in order to catch the ball. Given that the ball is landing six point eight three meters ahead of home base, that is the end of the solution. Thank you for watching

Our question says that a batter had to fly ball, which leaves the bat at 0.9 meters above the ground at an angle of 61 degrees with an initial velocity of 28 meters per second headed towards center field. Ignore air resistance. A how far from home plate with the ball land if it was not caught, and b the ball is caught by the centerfielder, who starts at a distance of 105 meters from home plate runs straight towards home plate at a constant speed. It makes the catch a ground level. What is his speed in order for him to be able to do this? So I wrote down here what? We're given V. Nona's 28 meters per second Fada, 61 degrees. The height of the ball hit off the bat a 0.9 meters. That's why not and for the first instance well, and even in the last one we consider to be a ground level and ground level zero, so are final value. Why zero? So the first thing we need to do to find out how far it goes if we know its initial velocity and its initial angle. We know V of X, so to find X when you know the time it travels. Okay, so the time it travels can be found by using. Why? Because people too. Why not? Plus the of wind of lost in the white direction times the time plus 1/2 acceleration in the wind direction times the Times Square. Okay, well, let's go ahead and simplify this. We know that. Why is zero So this is zero is equal to Why not? Plus be of why times the time minus 1/2 G. Because the acceleration in my direction is gravity In the minus y directions. This is minus 1/2 G comes the time squared. So if you want to solve for time we can use the quadratic formula. Pretty is going to be equal to, uh, minus v not signed. Data plus or minus the square root of Vina signed data in that square. So, Veena science data, Let's make this look more like a data area squared, Uh, minus four times minus 1/2 G multiplied by Why not? Okay. Oh, divided by two times minus 1/2 Chief. Okay, so now we have we know all the values that we need to plug in in this equation we have. Why not? 0.9 meters fada, 61 degrees V nonce, 28 meters per second. Gravity is 9.8 meters per second squared. So plug all those values in on your calculator and you'll find that you're gonna get two values for tea because the plus or minus one of them is five point 034 seconds. And the other one is that a common here? Minus, uh, 0.365 seconds. Well, we can't have minus time, so we're going to ignore that. We're going to use the positive time for our tea. So now, uh, we have X is equal to the of ex glossing extraction times T Okay, well, V of X is V not times that co sign Stada Times the time. Okay, well, for V, not you. Plug in 28 meters per second, multiply that by co sign of 61 degrees and then multiply that. By the time which we found to be 5.34 seconds, you'll find that the distance is 68 meters. So that's the solution to part a Okay, start a new page because for part B, it says, Well, the centerfielder starts at a position that was 105 meters away and sprints into where this ball is going to land and catches it right before he hits the ground. And they want you to know they want to know how fast he's going to be traveling in order to do that So his Velocity V would be equal to that distance that he's going to be covering divided by the time it would take him to cover it. Okay, that distance is the starting point 105 meters away, minus 68 because that's how far the ball goes so that the difference there is how far he needs to travel, divided by the time, which was 5.34 seconds. Okay, plug this into your calculator and this comes out to be a 7.3 meters per second. That's how fast the outfielder would need to run to get the ball

In the given problem. Ah, ballplayer, standing at a whole late suppose represented by this point a hits a baseball, which is Scott by another player at the same horizontal level. Suppose it is represented by the point B. The ball is being hit at an initial speed v I. It was from 22.0 meter per second and at an angle off 60 degree with the horizontal baseline. And then it is Scott at this point. B. But another player? No. Initially Speed re. I is given us 22.0 meter purse again. The angle with the horizontal is 60 degree in the first part off the problem we have to find How high will the ball rise? This is the man, seem, um, height. The ball really rise, which is given by an expression. We I square sign Square Tita divided by 40. So here we put all the values. The ice square means 22. I was glad. Sinus square 60 degree divided by two in 29.8, it will become for 84 into square off on the route tree by two, which is the value of science. 60 degree and whole spiral this and in the denominator it will be 19.6 so stiff. I find all these values I would be living behind. It will be leaving behind for me to calculate 3 63 divided by 19.6, which comes out to be 18.52 meter, which is the answer for the first part. Now, in the second part, we have to find how much time will elapse from the time the ball leaves the that. Until it reaches the killer means time off light off the ball. We have to fight, which is given by an expression to me. I signed Tita, divided by G Means do into 22 into signs 60 degree divided by 9.8 so it will become 44 in tow, fruit tree by two, divided by nine point day. So if I calculate it, it comes out to be 3.9 seconds, which is the answer for the second part. Now, in the lower part, we have to find the distance from home blade. The will the fielder be when he catches the ball means we have to find this distance between the through our and the fielder and this distances given again by an expression B I square sign. Do Tita, divided by G, means it becomes 22 whole square sign toe into 60 degree divided by 9.8. And if I put all these values, I will get value off 48 or 42.8 meter, which is a range which is the distance between the floor and the catcher. 42.8 meter, which is the answer for the car far.

So in the given problem they seem that mhm Amal is thrown at 26.6 and the angle with the horizontal is 15 a week And it is catched at some height which is one point. Mhm. Uh Okay. Uh this so article election height can be written by equation of motion as beauty minus half of G T square. Yeah So 0.914 can be written as 36.6. sign component 15- of half and yeah. T square. So simplifying this project in question we get five days square Bless 28.03 T minus. Yeah. So that this is also minus less. 0.91 4th exclusive. Yeah. So this is the form. No. Yeah we have to find the roots of this function which is mhm It is yeah minus of B plus minus route over B squared minus four A. C by two way. But here we will consider the plus plus value because we want the other end, we want when it is coming down so it will be the largest team. Love. It is so minus B. Yeah yeah minus the same sign we have to consider so we'll take mine as well. Yeah. So minus b minus off brutal. What Despair -4 a. c. right to it. Mhm. So the values already negative. So keeping keeping both sides knew- will be canceled. So it will be 20 8.03 plus route over 28.03. Holy Square four is 4 into five into .914 upon to to into five. So if you See it will be 28.03 less 27.7 x 10 which is nearly 55 by 10 or you can say 5.5 2nd approximately. So this is the time permitted to ball to be present here. So the person who is Going to catch the ball is now the distance of 110 m. So velocity to reach will be stands by time Because 2 1, 10 x 5.5 second, which will be okay, 20 m person can approximate. Yeah.


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