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ssm From the top of a tall building, a gun is fired. The bullet leaves the gun at a speed of 340 m/s, parallel to the ground. As the drawing shows, the bullet puts a hole in a window of another building and hits the wall that faces the window. Using the data in the drawing, determine the distances D and H, which locate the point where the gun was fired. Assume that the bullet does not slow down as it passes through the window.

31$m$850$m$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

Sinead D.

October 3, 2020

Samuel K.

April 8, 2021

Is time for horizontal and vertical motion equal? because i saw you substituting t on both motion

Alyssa J.

October 17, 2021

Yes, time for vertical and horizontal is the same. This is explained by the collision of the bullet occurring at the same time on both axes.

I calculated 870.82m for the D value.

University of Washington

Simon Fraser University

University of Sheffield

University of Winnipeg

Lectures

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2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

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A vector is a mathematical entity that has a magnitude (or length) and direction. The vector is represented by a line segment with a definite beginning, direction, and magnitude. Vectors are added by adding their respective components, and multiplied by a scalar (or a number) to scale the vector.

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so the question states that a bullet is shot at 340 meters per second and it passes through a window and then hits a wall and it drops 0.5 meters after it passes through the window and hits the wall and also moves a distance of 6.9 meters. And our task is to find what the value of H is as well as what the value of D is. So we know for a fact that the bullet drops 0.5 meters and it moves a total of 6.9 meters in the X direction during this time. So because this projectile motion and it tells you that the bullet doesn't slow down as it goes to the window, we can find the time it takes for the bullet to make the transition from the hole in the window to the wall. So to do this, we can say at the horizontal velocity of the bullet times. The time is equal to the displacement and the horizontal velocity of the bullet is 340 meters per second. We're trying to find T and we know that the displacement is 6.9 meters So the time it takes for the bullet to go from the hole in the in the window to the wall is 0.20 to 9 seconds. So now that we know this time, we can figure out what the vertical component of the velocity is of the bullet right when it enters the window. So to do this we can use another kid a magic formula which states that the change in displacement in the Y direction is equal to the, uh, initial velocity in the Y direction times the time close one have times the acceleration times, the time squared. So we know that the change in displacement is going to be 0.5 meters after it enters the the the whole in the window. We don't know what the velocity is in the Y direction. We know what the time it takes, though for toe passed through the window, the whole in the window, and hit the A spot on the wall which is 0.0 20 to 9 seconds. We know that the acceleration is equal to negative 9.8 meters per second squared. And once again, we know what the time is 0.20 to 9 seconds were squaring that So when we saw for the vertical component of the velocity which we called the not which it really should be Visa. Uh, why we get that the ah vertical component is equal to negative 24 0.5 three a meters per second. So now that we're given what the vertical component of the velocity is at the time that the bullet passes through the hole here, that's 0.5 meters up. We can use once again arcana Matic formulas to figure out how, um far the bullet was displaced from when it was shot. So the equation we need to use is one that states that the final velocity squared is equal to the initial velocity squared, plus two times the acceleration times, the change in displacement or called out of line. So we know that the final velocity is going to be equal to negative 24.538 squared. We know that the initial velocity in the critical direction is zero. So this term cancels out and we know that the acceleration is negative 9.8 and we're trying to find Delta y. And so when we solve this, we find that Delta Y is equal to 30 0.72 meters. Um and when we do the calculation, it will be negative. But we can just take it as a positive number because we're just trying to find the magnitude of the height. So the 30.72 meters is this height right here, the height from the top of the building to the entry hole. And h is this this height here plus 0.5 meters. So we need to add 0.5 meters here. And when we do this, we find that H is equal to approximately 31 meters. So that is how you find age. Now, if we want to find are, um Devalue, we need to We need to find how long it takes for the bullet to enter the the whole. So to do this, we can take our velocity that we know, uh, the vertical component of the velocity that we knew when it enters the whole, which is negative 24.538 And use the kinetic equation which states that the final velocity is equal to the initial lost e plus the acceleration times the time. So we're going to say that the final velocity in this case when it right when it enters the hole in the vertical direction is negative 24.538 meters per second. The initial velocity is just zero because Ebola is being shut out horizontally and the acceleration is negative 9.8 times t. So when we saw for tea, we get that the time that it takes for the bullet to go from the top of the building to the hole is 2.5 seconds. And using this, we can figure out how far the bullet travels by using the equation which states that the horizontal velocity times a time is equal to the range. The horizontal velocity in this case is 340 meters per second. The time it takes to get to the hole in the wall is 2.52 point five seconds. So the total range is 850 meters. And that is the, uh our devalue

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