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(II) Students shoot a plastic ball horizontally from a projectile launcher. They measure the distance $x$ the ball travels horizontally, the distance $y$ the ball falls vertically, and the total time $t$ the ball is in the air for six different heights of the projectile launcher. Here is their data.(a) Determine the best-fit straight line that represents $x$ as a function of $t .$ What is the initial speed of the ball obtained from the best-fit straight line? (b) Determine the best-fit quadratic cquation that represents $y$ as a function of $t$ t. What is the acceleration of the ball in the vertical direction?

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a) $x=(3.03 t-0.0265) \mathrm{m}$, $3.03 \mathrm{m} / \mathrm{s}$b) $y=\left(0.158-0.855 t+6.09 t^{2}\right) \mathrm{m}$, $12.2 \mathrm{m} / \mathrm{s}^{2}$

Physics 101 Mechanics

Chapter 3

Kinematics in Two or Three Dimensions; Vectors

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Rutgers, The State University of New Jersey

Simon Fraser University

Hope College

University of Winnipeg

Lectures

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

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In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

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Projectile Motion Bob thro…

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So here we need to determine the best fit report a best fit straight line. Ah, you can use any, um, graphical software, Second Excel or Matt Lab in order to find the best fit straight line. Basically, you're trying to find a linear regression for the data I would recommend using s Excel because it's the best. I would say it's the most user friendly for this type of thing. And so when you plug in the data in excel of the equation is gonna be ex equaling 3.3 t minus 0.265 meters. So that would be the units. We know that the initial speed of the ball is the X component of velocity, which from this equation would be 3.3 meters per second squared so we can save the ex Initial would be equal to 3.3 meters per second. Ah, and, uh, this is simply equal to m X plus Be so this be should be a very small number, because you shouldn't really start at a negative exposition. You should always be starting at ah, because it's an exposition of zero. So this should be pretty small in that case on. And if you were to graph it, uh, the graph would look like this. So this would be the best best fit, straight line and then four part B. Ah, we want to find the best fit quadratic equation. And again, I would say using Excel. It's, ah again best user friendly for this type of ah problem. And we find that why would be equal to 0.158 minus 0.855 t plus 6.9 t squared again, the units would be in meters. Since the quadratic term in this relationship is 1/2 a t squared, we can say that 6.9 t squared would be equal to 1/2 a t squared. Uh, let's eliminate the T squared and we find it would be approximately 12.18 meters per second squared, so I'd be the acceleration for this. And then, if you were to graph it using excel Ah, this is what the graph would look like again on R squared value of 0.9989 That's extremely good as closest you can get to one. Ah, that would be one is essentially a perfect agreement. It's usually not possible. So 0.9989 is extremely good agreement. So I would say that's the more accurate. Um Ah. Best fit would be a quadratic fit instead of a linear fit. So here you always want to take a take into account that r squared value. The closer it is to one of the better, the better the model is. And in this case, the better model would, of course, be the quadratic sit. That is the end of the solution. Thank you for watching.

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