query 21

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course Phy 231

3/23 1:15

021. `query 21

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Question: `q 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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Your solution:

We begin by working in the vertical direction. Assuming the initial vertical velocity is zero and the the only force acting vertically on the object is graviy (with its known acceleration of 9.8m/s^2), we can determine the final vertical velocity using the equation vf^2=v0^2+2a`ds.

Final vertical velocity can tell us average vertical velocity (if acceleration is uniform, which we assume for this case) by adding initial and final velocity and dividing by 2. Then we can determine the length of time the object is in the air, using the equation vAve=`ds/`dt, applied to the vertical direction.

Now we can see how far the object moves in the horizontal direction, using given horizontal velocity and `dt.

Using the horizontal and vertical velocity vectors, we can determine the angle of the two vectors by calculating the arctan(vy/vx).

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Given Solution:

`a** 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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Self-critique (if necessary):

Something I'm confused about-- the horizontal velocity vector is constant, but the vertical velocity vector is constantly changing. Doesn't that affect our results? Do we use average velocity for the vector, then?

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Question: `qGive 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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Your solution:

1) The force of gravity on an object positioned on an incline needs to be separated into horizontal and vertical components in order to be of use to us. Of course, gravity is itself totally vertical, so the directions we're really separating out are parallel to the incline and perpendicular to it. As for magnitude, that tells us the portion of gravity's force that is working in that direction.

2) If an object is propelled by an initial force along a certain path and then encounters a force in a particular direction, separating out the vertical and horizontal components of the second force allows us to determine what that will do to the velocity (both magnitude and direction) of the object. The component of the force parallel to the object's original path will either speed or slow the object. The component of the force perpendicular to the object's original path will cause it to change direction. The angle of the force will determine the new direction.

3) A projectile directed at an angle above the x-axis; the vertical vector will tell us exactly how high the projectile will go before beginning to fall, and the horizontal vector will tell us its horizontal velocity, necessary in determining eventual landing position.

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Given Solution:

`a

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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&#Very good responses. Let me know if you have questions. &#