PHY201 Query 21

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course PHY 201

9:30 PM on 4/2/13

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:

 

 First, since we know that the vertical displacement, and that the vertical initial velocity is 0 m/s and that the acceleration is equal to gravity which is equal to 9.8 m/s, we can use either the vf^2 = v0^2 + 2a'dy equation to solve for final vertical velocity and use the equation 'dt = 'dv / a to find time, or use the equation 'dy = v0t + 0.5at^2. Once we solve for the time interval in the vertical motion we can then begin to solve for the horizontal direction.

The initial vertical horizontal velocity is equal to the final and average horizontal velocities. Therefore, we could use the basic equation vAve = 'dx / 'dt and solve for 'dx to get the final position.

Now, when it comes to velocity vectors, we just solve for the vertical final velocity. Plot the vectors in the x and y directions. Once this is solved, we can solve for the total magnitude by using pythagoreans theorem magnitude = sqrt(x^2 + y^2) and the angle of motion as tan^-1 (y / x).

 

 

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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):

 

 

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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:

 

From Idea 12, three examples of vector quantities are acceleration, force, and displacement.

If we have an x and y component, we can then find the resultant component of the vector and the angle. If we are given a vector with magnitude and angle we can solve for the x and y components.

 

 

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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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