Problem 19 Medium Difficulty

A batted baseball leaves the bat at an angle of $30.0^{\circ}$ above the horizontal and is caught by an outfielder 375 ft from home plate at the same height from which it left the bat. (a) What was the initial speed of the ball? (b) How high does the ball rise above the point where it struck the bat?

Answer

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Video Transcript

the hardest until displacement, when the bald returns to its original height is given by our acquittal The non spares times signe to Tama For what? When we noticed the initial velocity. Teton art is the angle with the horizontal with the angle off the initial velocity with the horizontal Andy's the magnitude ofthe the acceleration. And so this is so this genius basically 9.8 meters per second squared on we have at maximum height, Viv, I issue because the motion is completely horizontal. So we will use the same question and this side for five. Sorry for the night. So he was a desecration of what he every knot is going to be quiet our times t over, sign off twice, not have to take over on DH. Notice that you're odd. No, um which is also called The range is given in feet on acceleration and gravity is usually taken tto be immutable. Second scare. So you might you are in need. So you want to convert our fate into meter. All right, me that into feet could be consistent with the units. So they're using Case is converting feet into meet us. But just for a change I'm gonna use on the value ofthe tea in feet per second scare. So I have already done the kind of conversion over here. So I'm going to use that. You can also kind. What? Meet a bus second. Sorry. You can also choose to convert this value of feet into a meter on. You'll get your velocity in unit itself, meet up a second like and is doing this for it in't. This is a greater 32 second school 16. I noticed that this is a jail, not a right. So we just need to take the positive part ofthe acceleration. So we saw this equation and we find the magnitude ofthe the initial velocity to be 118 feet per second. Now for five days. Since we have the company off the initial velocity along, why did accent of equal to be not sign off tonight? And this musical 59 my second. Not to find the height, we will lose the kind of medical questions that's connects the initial and final velocity acceleration on DH there, distance juggle. So we will use Mr Question and the reason the ideas in this equation is that we don't. You don't have to separately. Find time. And you already have all the values that you need to solve this equation. So this gives y minus. Why not to be quite a lot lice, grad. Linus. Not really scratch. All right. Do we like now? I Maximum height, we by asio So this gives minus right. Do you like this? Is it Quentin? Get it off. 59. Sorry. Second hole squared over two times a wife. It is minus D. And that's what this is a cool minus. All types don't Five seconds, Graham. And this gives. So I minus y I know to be quick 54 by forfeit. So one thing that I want you to notice is that at maximum white V by my physio. But the neck velocity will is not called a zero because there is still some component for philosophy along X direction on along extra election. The ball has a constant horizontal confident of velocity because there is no acceleration along the X direction