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(1I) Revisit Example 9 of "Kinematics in Two or Three Dimensions; Vectors," and assume that the boy with the slingshot is below the boy in the tree (Fig. 45) and so aims upuard, directly at the boy in the tree. Show that again the boy in the trec makes the wrong move by letting go at the moment the water balloon is shot.
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the boy and the balloon will collide
Physics 101 Mechanics
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
November 2, 2020
Rutgers, The State University of New Jersey
University of Michigan - Ann Arbor
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.
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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so we can draw a diagram of the system. Aah! This would be the direction of the velocity initial. Ah, we could say that this would be the height h Ah, we can say that this is a distance D. This is the Y axis. This would, of course, be the X axis. And we have some angle of launch data. And so we have Thio see, essentially find the, um, height of the boy and the height of the balloon at a certain time. So we can say that the exposition of the balloon is going to be equal to be initial co sign data times T we can say that the Y position of the balloon will be equal to, um, the initial sign of theta times. Teeth minus 1/2 G t squared and we can sit at the Y position of the boy is gonna be well to H minus 1/2 GT squared. So we can say that we're going to use the horizontal motion at constant velocity in order to find the elapsed time after balloon after the balloon has traveled. Ah, a distance d to the right. So we can say d equals the initial times co sign of feta times, He ah, we can say t sub d. Um And so we can say that T de Sol for t d. This is gonna equal be over the initial co sign of data. So at that time, where is the balloon? So we can say that why of the balloon would then be equal to be again the initial signs of fate a t d minus half g t d squared. So we would essentially plug this into this equation for why balloon and we get the initial sign of data and then times d over the initial co sign of data. And then we're going to save minus 1/2 g, uh, multiplied by v initial co sign of Data de Quantity squared. And this is gonna equal d tangent of theta minus, uh, g over too times we can simply say the initial co sign of data for the denominator de quantity squared. And so, at this point, we have to stay after we find that where is the boy vertically at this time? So we can say why of the boy legal again. H minus 1/2 g t sub d squared. This is gonna equal de tangent of Fada minus again G over two times G over the initial co sign of theta quantity squared. And as you can see, this is exactly equal to the Y position of the balloon. Which means that if at a certain time the same, why position the boy and balloon will collide. So that's why it is not smart for the boy to ah, throw the balloon as soon as he jumps off. Because then they'll be at the same Y position. Um and they're going to essentially, they will. The boy will hit. The boy will be hit by the balloon. That is our final answer. That is the end of the solution. Thank you for watching.
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