14“Study of the flight distance-angle of departure relationship”

Safety procedures

1. Follow directions. Come to lab prepared to perform the experiment. Follow all written and verbal instructions. When in doubt, ask.
2. Absolutely no horseplay. Be alert and attentive at all times. Actlikeanadult.
3. Report all accidents, injuries or breakage to the instructor immediately. Also, reportanyequipmentthatyoususpectismalfunctioning.
4. Dress appropriately. Avoid wearing overly-bulky or loose-fitting clothing, or dangling jewelry that may become entangled in your experimental apparatus. Pin or tie back long hair and roll up loose sleeves.
5. Usegoggles:
1. whenheatinganything.
2. when using any type of projectile.
3. when instructed to do so.
6. Use equipment with care for the purpose for which it is intended.
7. Do not perform unauthorized experiments. Get the instructor's permission before you try something original.
8. Be careful when working with apparatus that may be hot. If you must pick it up, use tongs, a wet paper towel, or other appropriate holder.
9. If a thermometer breaks, inform the instructor immediately. Do not touch either the broken glass or the mercury with your bare skin.
10. Ask the instructor to check all electrical circuits before you turn on the power.
11. When working with electrical circuits, be sure that the current is turned off before making adjustments in the circuit.
12. Do not connect the terminals of a battery or power supply to each other with a wire. Such a wirewillbecomedangerouslyhot.
13. Return all equipment, clean and in good condition, to the designated location at the end of the lab period.
14. Leave your lab area cleaner than you found it.

Additional differentiated tasks and problems

Problem 1

A pool ball leaves a 0.60-meter high table with an initial horizontal velocity of 2.4 m/s. Predict the time required for the pool ball to fall to the ground and the horizontal distance between the table's edge and the ball's landing location.

Problem 2

A soccer ball is kicked horizontally off a 22.0-meter high hill and lands a distance of 35.0 meters from the edge of the hill. Determine the initial horizontal velocity of the soccer ball.

Problem 3

A football is kicked with an initial velocity of 25 m/s at an angle of 45-degrees with the horizontal. Determine the time of flight, the horizontal distance, and the peak height of the football.

Problem 4

A long jumper leaves the ground with an initial velocity of 12 m/s at an angle of 28-degrees above the horizontal. Determine the time of flight, the horizontal distance, and the peak height of the long-jumper.

Solutions for additional problems

The solution of this problem begins by equating the known or given values with the symbols of the kinematic equations - x, y, v_ix, v_iy, a_x, a_y, and t. Because horizontal and vertical information is used separately, it is a wise idea to organized the given information in two columns - one column for horizontal information and one column for vertical information. In this case, the following information is either given or implied in the problem statement:

As indicated in the table, the unknown quantity is the horizontal displacement (and the time of flight) of the pool ball. The solution of the problem now requires the selection of an appropriate strategy for using the kinematic equations and the known information to solve for the unknown quantities. It will almost always be the case that such a strategy demands that one of the vertical equations be used to determine the time of flight of the projectile and then one of the horizontal equations be used to find the other unknown quantities (or vice versa - first use the horizontal and then the vertical equation). An organized listing of known quantities (as in the table above) provides cues for the selection of the strategy. For example, the table above reveals that there are three quantities known about the vertical motion of the pool ball. Since each equation has four variables in it, knowledge of three of the variables allows one to calculate a fourth variable. Thus, it would be reasonable that a vertical equation is used with the vertical values to determine time and then the horizontal equations be used to determine the horizontal displacement (x). The first vertical equation (y = v_iy•t +0.5•a_y•t²) will allow for the determination of the time. Once the appropriate equation has been selected, the physics problem becomes transformed into an algebra problem. By substitution of known values, the equation takes the form of

-0.60 m = (0 m/s)•t + 0.5•(-9.8 m/s/s)•t²

Since the first term on the right side of the equation reduces to 0, the equation can be simplified to

-0.60 m = (-4.9 m/s/s)•t²

If both sides of the equation are divided by -5.0 m/s/s, the equation becomes

0.122 s² = t²

By taking the square root of both sides of the equation, the time of flight can then be determined.

t = 0.350 s (rounded from 0.3499 s)

Once the time has been determined, a horizontal equation can be used to determine the horizontal displacement of the pool ball. Recall from the given information, v_ix = 2.4 m/s and a_x = 0 m/s/s. The first horizontal equation (x = v_ix•t + 0.5•a_x•t²) can then be used to solve for "x." With the equation selected, the physics problem once more becomes transformed into an algebra problem. By substitution of known values, the equation takes the form of

x = (2.4 m/s)•(0.3499 s) + 0.5•(0 m/s/s)•(0.3499 s)²

Since the second term on the right side of the equation reduces to 0, the equation can then be simplified to

x = (2.4 m/s)•(0.3499 s)

Thus,

x = 0.84 m (rounded from 0.8398 m)

The answer to the stated problem is that the pool ball is in the air for 0.35 seconds and lands a horizontal distance of 0.84 m from the edge of the pool table.

Guide on solving problems on projectile motion

The following procedure summarizes the above problem-solving approach.

·         Carefully read the problem and list known and unknown information in terms of the symbols of the kinematic equations. For convenience sake, make a table with horizontal information on one side and vertical information on the other side.

·         Identify the unknown quantity that the problem requests you to solve for.

·         Select either a horizontal or vertical equation to solve for the time of flight of the projectile.

·         With the time determined, use one of the other equations to solve for the unknown. (Usually, if a horizontal equation is used to solve for time, then a vertical equation can be used to solve for the final unknown quantity.)

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