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A soccer player kicks ball with speed of 24.0!/s atan angle of 18.09 above the horizontal_ She sees the ball hit the on the side of a hill 25.0 meters away. Draw di...

Question

A soccer player kicks ball with speed of 24.0!/s atan angle of 18.09 above the horizontal_ She sees the ball hit the on the side of a hill 25.0 meters away. Draw diagram of the situation indicating distances and the path Of the ball.Determine the time of flightb. Determine the height of the ball as it lands on the hill.d. Determine the final velocity and angle of impact (put the angle on your diagram).

A soccer player kicks ball with speed of 24.0!/s atan angle of 18.09 above the horizontal_ She sees the ball hit the on the side of a hill 25.0 meters away. Draw diagram of the situation indicating distances and the path Of the ball. Determine the time of flight b. Determine the height of the ball as it lands on the hill. d. Determine the final velocity and angle of impact (put the angle on your diagram).



Answers

A soccer player $20.0 \mathrm{~m}$ from the goal stands ready to score. In the way stands a goalkeeper, $1.70 \mathrm{~m}$ tall and $5.00 \mathrm{~m}$ out from the goal, whose crossbar is at $2.44 \mathrm{~m}$ high. The striker kicks the ball toward the goal at $18 \mathrm{~m} / \mathrm{s}$. Determine whether the ball makes it over the goalkeeper and/or over the goal for each of the following launch angles (above the horizontal): (a) $20^{\circ}$; (b) $25^{\circ}$; (c) $30^{\circ}$.

Initial speed is given 16 m per second at an angle 28 degree from the This 16 m per second and angle is 28 degrees, half of the horizontal out of the ground. We have to find the speed of the wall. Then the goalie cages in it in front of the net. So we know that the distances 16.8 metre. This distance is 16 8.2 m. So first we will try to find the time to cover this distance. We know that access they called V X into T. That means distance covered in X direction is 16.8. Velocity in X direction is velocity is 16 m per second in X direction cost. 28. This is the X component of velocity in two times. So from here, time should be equal to 16.8. Divided by 16 costs 28 16.8 divided by 16 into costs 28 This is equal to one point 18 nine seconds. This time is equal to 1.19 seconds. So after the stain, suppose it has a speed v this direction. So we know that the X confident of this velocity and by component of this velocity, VX will be same. This V X will be equal to 16 cost 28 right. So this is equal to 16 into cost 28 14 point 13 m per second. Now we can also find we We know that we finally is equal to the initial plus exploration into t. So here we will apply the situation in the right direction only. So viva is the final is V by equal to the initial in the Y direction will be 16 sign 28 plus exhalation is minus 9.81 At the time, we had already known it's just 1.189 So multiply with 1.189 So this week I will be equal to 16 into sign 28 minus 9.81 into one point 189 So this is equal to minus 4.152 m per second. This negative science so that the direction of this confident in the downward direction or as we can see in the diagram also this is very high. So we know that this is speed will be equal 200 V X square, plus we ve square so the speed will be equal to and the road v X, which is 14.13 squared plus vive i which is 4.152 4.15 to square. This is equal to 14.73 m per second. This is the speed off the ball when he gets it. Now we have to find the angle also So we can say that this angle, as opposed to 2010 hitter, will be equal to we've I v X. So this theater will be called to 10 and worse we by which is 4.15 to the worldwide, 14.13 So this angle is equal to four point 152 divided by 14.13 This is 16.37 degrees below the horizontal

Can this question we have to find out the speed of the ball. Win the goalie cages it. So the range is given is change is giving us A 16 by an eight m. And The ball make an angle of 28. They were with the ground an initial velocity of the ball, his 16 m per second. So the initial component of the velocities are in asia component, initial component velocities. We're not. Yes it will do. We're not Constanta. So we not X. Is it well too 16 of course 28 degree. So we're not. The presented component become 14.1 meter per second. And the vertical component become we not by is equal to be not scientific. So we're not for is it will do 16 side 28 degree. So we advise it well too seven by five meter per second. So the time of like dime of flight becomes eggs. Is it? Well too, we not accent too. This X. Is range which is a world too No way of X into A. D. So T. Is equal to are divided by movie. No takes. So we get DS. This is 16 by an eight m Divide by 14 5 one m Sooty We get is 1.1 night the second. And to find out what we buy. We were is equal to we not by minus G. D. So this we were is even too seven by five minus 9.8. Multiply by I want to apply by one pine 1 nine seconds. So we why is it well too -4 x two meter per second. All right. The final speed is given us final speed. He's given us. We is equal to undo rude. We X scared plus we've I scare so we is equal to and rude. 14 x one scared. Bless minus fall by too scared. So we will get this. And route two 116 Buying five m scare second scare. So we is it going to 14.7 meters per second?

So the question states that a person kicks a soccer ball at 16 meters per second, an angle of 28 degrees, and a goalie catches a ball that 16.8 meters away. And we're trying to find what the velocity of the ball is when the goalkeeper catches it. So the first thing we really should do is break up this initial velocity vector into components so into a V of X and a V of why component we confined Visa Becks, because we know that co sign of 28 degrees is equal to, uh, adjacent over iPod knees and the adjacent. In his case, his visa vex. So Visa backs over 16 which means Visa. Becks is equal to 16 co sign 28 degrees, and the same thing goes for resupply. Except instead of a co sign. It's a sign so we'll get that pizza. Why is equal to 16 times sign of 28 degrees? So now that we know this, uh, we should try and find how long the ball is in the air. Four. So to do this, we can take our visa, Becks. And because there's no acceleration in the X direction. We can multiply it by t, and this will give us our displacement in the X direction. So there's no acceleration term in this formula. So when we plug in Visa, Becks and Delta X, which is 16.8 meters, we find that T is around 1.1891 seconds. And so this is gonna be important when solving for, um, our vertical component of the velocity. So if we if we look at the final velocity of the ball when the goalkeeper catches it, we know for effect that the horizontal component of the velocity is going to stay constant because it's project out motion. There's no acceleration, as we said earlier, so the horizontal velocity is going to be 16 times co sign of 28 degrees. Now, of course, we're trying to find the vertical component eso weaken, solve for the total velocity of the bomb. Now that we know the time, we can just use a cinematic equation to solve for this vertical lost e. So we're going to use the one that states that the final velocity is equal to the initial lost E plus the acceleration times the time so you don't know what the final US is. We know that the initial velocity in the vertical direction is 16 times sign of 28 degrees. We also know that the acceleration is equal to negative 9.8 meters per second squared due to gravity. And we also know the Time T is 1.18 91 seconds. So when we saw for V, we get that he v should really be visa. Why? Which is this question? Mark is equal to negative 4.14 to 6 meters per second. And now all we really have to do is protect your in here in the salt for this Capital V Here. Um, when we work out 16 times coastline of 20 degrees, we get that visa of ex is equal to 14.12716 meters per second. And now that we know Visa, Becks and Visa, why weaken Take thes square root of visa X squared plus visa y squared. This will just give us our capital V and when we put this in, we find that capital V is equal to 14 0.72 meters per second

The distance that we want the ball to travel in the X direction is 16.8 m. The initial speed is 16 meters per second and the angle Is 28°. Okay, what's the speed when the goalie catches it? Well, mm hmm. The squared equals v initial squared plus two. Uh, G delta Y or minus two. G. Delta Y. Okay. So this would apply in the Y direction. So V Y is what we're trying to figure out. V zero, Y is V zero sign data, Delta Y is zero. Oh, no, no, no, no, no, no, no. Delta Y is going to change. Sorry. Okay. So I would need to know the height of the ball if I'm going to use this. So let's try a different approach. Um, we know what V. X is going to be. We just need to figure out V. Y. Um, Mhm X Equals or X two equals V zero. Co sign theta times T. So T is going to be X two over V. Zero cosign Theta. So I can put that into a calculator. Um T. E. Equals V. Let me put in what? I know V. Zero Equals 16. X two is 16.8 feed A. Is 28. Okay. D. Equals X. Two over V. Zero cosign Theta. Okay so what's my problem? Um V. Zero. Okay. I didn't put the v. zero in the right spot here. Okay that's 1.19 seconds. So um and I didn't need this. It's gonna be easier to use V. So why equals the uh zero co sign nope sign minus G. T. And now we know T. So Visa Y. Equals v. zero signed data -GT. Putting that into a calculator. I get negative 4.15. Now X. V. X. Doesn't change. It's just going to be V. Zero co sign data because there's no acceleration in the X direction. Mm That's 14.12. Okay, speed. So all we have to do is the square root of the two. So square root of v y squared. Mhm. Okay. Plus V X squared 14 point yeah, seven meters per second. Let's check that in the back of the book. And that's correct. Thank you.


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