course Phy 231 ???????~???assignment #021??~M????€????????Physics I
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14:11:08 Explain how to obtain the final speed and direction of motion of a projectile which starts with known velocity in the horizontal direction and falls a known vertical distance, using the analysis of vertical and horizontal motion and vectors.
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RESPONSE --> We use the acceleration of the Earth as 9.8 m/s^2 to determine the final velocity at the moment of impact with the equation of vyf = 'sqrt ( 2 * a * 'ds). This allows us to determine the magnitude of the final velocity by the equation of 'sqrt (vy^2 + vx^2) = vf, which will also give us the direction by using arctan ( y/ x ) = theta below the x-axis which can add 360 degrees to find the value of direction with respect to the x-axis using counter-clockwise rotation.
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14:11:36 ** The horizontal velocity is unchanging so the horizontal component is always equal to the known initial horizontal velocity. The vertical velocity starts at 0, with acceleration thru a known distance at 9.8 m/s^2 downward. The final vertical velocity is easily found using the fourth equation of motion. We therefore know the x (horizontal) and y (vertical) components of the velocity. Using the Pythagorean Theorem and arctan (vy / vx) we find the speed and direction of the motion. **
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RESPONSE --> Ok
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14:19:02 Give at least three examples of vector quantities for which we might wish to find the components from magnitude and direction. Explain the meaning of the magnitude and the direction of each, and explain the meaning of the vector components.
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RESPONSE --> We could have a toy car sliding off of a table that gives us a final direction and magnitude in a series of trials of 5 m/s at 340 degrees, 5.2 m/s at 335 degrees, and 4.65 m/s at 347 degrees. This tells us that the toy car was traveling at the moment of impact with each of these corresponding velocities in the directions given. We would then have vector components for velocity in the horizontal and vertical directions determined by the magnitude * cos (theta) and magnitude * sin (theta) respectively.
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14:19:20 ** GOOD STUDENT RESPONSE: Examples might include: A force acting on an object causing it to move in an angular direction. A ball falling to the ground with a certain velocity and angle. A two car collision; velocity and momentum are both vector quantities and both important for analyzing the collision.. The magnitude and directiohn of the relsultant is the velocity and direction of travel. The vector components are the horizontal and vertical components that would produce the same effect as the resultant.
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RESPONSE --> Ok
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