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(II) You buy a plastic dart gun, and being a clever physicsstudent you decide to do a quick calculation to findits maximum horizontal range. You shoot the gun straightup, and it takes 4.0 s for the dart to land back at the barrel.What is the maximum horizontal range of your gun?
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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
Rutgers, The State University of New Jersey
University of Winnipeg
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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Our question says that you buy a plastic dart gun and being a clever physics student, you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up and it takes four seconds for the dark tow land back at the barrel. What's the maximum horizontal range of your gun? Okay, for this problem, I, um I say that when shooting the gun vertically half of the time of flight is spent moving upwards, right? Thus, the upwards flight will take about two seconds. Okay? And I'm going to choose upwards to be in the positive y direction since at the top of the flight, the velocity, the vertical velocity is zero. Okay, so I write down what we were given here were what were given here and that is the initial point which were choosing is Y 00 is equal to zero. The velocity is entirely in the UAE direction. Okay, t, the total time of flight is four seconds, right? And at the peak, the velocity and the Y direction is going to be zero, right? It's no longer accelerating upwards is about to start accelerating downwards. Okay. And that acceleration is minus 9.8 meters per second cause it's accelerating down towards the ground. And we define positive wise up. Okay. So we can go ahead and then use equation to dash 12 from two Dutch 12 a. Excuse me from our book which says that the velocity v of y at a point is equal to the initial velocity B Y zero close the acceleration here times the time. Okay, well, we want time here. Right? But our time is the time it takes for it to get to the top. So we're going to label this as t sub t for top. Okay, Time some tea for the time it takes to get to the top. All right. I'm sorry. We don't want to solve for sub t. We know what the time it takes is for it to get to the top. We want to solve for the y of zero we want to solve for the initial velocity. Because if you know the initial velocity and the wider action, we can calculate the initial velocity that would be required in the ex direction because it's just gonna be the velocity out of the barrel of the gun if it's shot horizontally. So t 70 climbs acceleration. Here is the acceleration in the white direction. This is equal to, um minus ve y zero right, Because the of lie at the top, which is what we're considering is equal to zero, so we can ignore that. Okay, so therefore the Y of zero is equal to minus a of y times the time it takes for it to get to the top. Okay, No, The time it takes for it to get to the top is 1/2 that of the total time. And the acceleration in the white direction is minus 9.8 meters per second. So minus and minus is plus because this is positive 9.8 and that's meters per second squared. And that's multiplied by four, divided by two, which is two seconds. We can write this up here actually say that that he at the top is equal to one has t. Okay. And if you carry this out, you find this equals 19.6 meters per second. Okay, Now that we have that, we can use our range formula which says that the range something is going to travel is going to be equal to the initial velocity. Right? Squared Time's sign of two times the initial angle at which it's launched, divided by gravity. Gravitational acceleration. Okay, well, our the our initial velocity, which we just found for why can also be applied to X because in this case, the student shot it straight up in the air. So all the velocity was in the white direction. So the initial velocity out of the barrel of a gun now is all going to be in the ex direction. So this is going to be equal to 19.6 meters per second. That value squared, okay. And then sign to fate A. Well, if we're launching it horizontally, Okay, Data they did not then will be 45 degrees. So two times 45 is 90 degrees. So says sign of 90 degrees, divided by 9.8 meters per second script and putting years per second squared. Okay, Now, if you carry out this calculation, you find that the range is 39 years
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