course PHY201 ??x???????????assignment #021
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14:41:36 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 know horizontal velocity, acceleration, and v0(vert), and `ds(vert). We need to find vf(vert) to know the magnitude of the y component of the resultant. We already know the x component which is equal to horizontal velocity. using vf = sqrt( v0^2 + 2a`ds) Once we know the magnitude of the y direction we can figure out the resultant vector by using: ResultMagnitude = sqrt(vfHoriz^2 + vfVert^2) ResultAngle = arctan(vfVert/vfHoriz) + 360
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14:41:41
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14:44:28 ** 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 --> I think I misplaced the + 360. This is the kind of thing that I would have caught by commonsense in a real world situation, but I missed it here.
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14:52:29 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 --> A raqcuetball hitting a wall. In this case the y component would be the downward or upward motion, which would result in either an upward or downward spin off the wall. The x component would be perpendicular speed to the wall which would tell us how fast the ball would rebound off the wall. The motion of a frisbee as it flies through the air. Where the x component is the ground speed of the frisbee and the y component is its vertical velocity. The motion of an arrow flying through the air. The y represents the vertical direction and the x represents the ground speed of the arrow.
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14:52:49 ** 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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