Query 21

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course PHY 241

12/13 3

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:

Given v_x and `ds_y, know v_0_y = 0 m/s and a = 9.8 m/s^2 downwards.

Use v_f_y = sqrt(2*a*`ds_y) to find v_f_y.

Use v_f_y^2 + v_x^2 = v_r^2 to find resultant velocity, use arctan(v_f_y / v_x) to find direction

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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):ok

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Self-critique Rating:3

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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:

Velocity of a projectile

Acceleration of a car

Force acting on a mass hung from a pulley.

Magnitude is the amount of velocity, acceleration, or force, respectively. Direction tells in direction of motion, direction of acceleration (Whether the car is

speeding up or slowing down), or the sense of the force acting on the mass. The components represent pieces of the vector acting in certain directions, and can be used

to determine a resultant vector.

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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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Self-critique (if necessary):ok

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Self-critique Rating:3

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Self-critique (if necessary):

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Self-critique rating:

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