1. Go to http://www.physicsclassroom.com/Physics-Interactives/Vectors-andProjectiles/Projectile-Simulator then choose “Launch Interactive.”
2. Set the initial projectile speed to 25 m/s, the angle to 25°, and the height to 0 m.
a. Using the initial velocity, angle, and height, calculate the time and the range you expect the projectile to cover. Sketch a picture of the path you expect the projectile to cover.
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O , 0 and
Calculation of the time
0
Calculate range
Range = o
Sketch a picture of the path you expect the projectile to cover.
b. Press “trace path” and then start on the simulation. Sketch the path over your prediction in a contrasting color. Does the shape of the path fit your expectation? Record both the range and the time. Do they agree with your answers to part a? Why/why not?
The path trace after the simulation is as shown above. From the simulation,
The values obtained from the calculation and those obtained from the simulation were very close. I agree with the values as the simulation has provided the same answers.
3. Double the initial velocity to 50 m/s, and set the angle to 25°, and the height to 0 m.
a. Calculate both the expected time and range of the projectile. Do you expect the range to double?
0
Range = o
As a result of squaring the velocity, I do not expect the range to double. I expect it to increase by a multiplying factor but not twice.
b. Press start on the simulation. Record your range and time. How does the range change compared to step #2? Does the range double?
The range obtained is almost 4 times the one obtained in question 2.
4. Using trial and error with the simulation, find another angle measure that produces the same range as step 3. Record the angles tried and their ranges, in a neat table.
|
Angle (degree) |
Range (m) |
|
15 |
127.56 |
|
45 |
255.11 |
|
65 |
195.42 |
|
85 |
44.3 |
The angle that produces the same range as that in step is 65 o . The angles are related in that the sine of one angle equals the cosine of the other i.e.
Sin 25 0 = Cos 65 0 , and vice versa.
5. Keep the simulation set as it is. a. Using your answers to steps 3 & 4, predict another set of 2 angles that will produce the same range as each other. Write the angles in your lab notebook, and explain why you chose that pair.
Another set of angles that will produce the same range are;
15 0 and 75 0
30 0 and 60 0
I chose these pair of angles because the sine of one angle equals the cosine of the other. As concluded in step 4, a pair of angles where the sine of one of the angles equals the cosine of the other produces the same range, i.e.
b. Calculate the theoretical range for one of the angles using the initial velocity, each angle and the height while your partner does the calculation for the other angle. Compare your answers. If they are not the same, check each other’s work and/or go back to step 5a.
Calculate the theoretical range
1 st angle: Range = o
2 nd angle: Range = o
The answers obtained are the same.
c. Set the simulation angle for the first angle and press start. Record the actual time and range. Repeat with the second angle.
Simulation of 1 st angle:
Simulation of 2 nd angle:
Do the values agree with your predictions? Why/why not?
The values obtained from the simulation are approximately the same as those derived from the theoretical calculations.
How is the angle you chose related to the angle used in step 3? Explain
The angle I chose is not equal to the one in step 3. Both angles produce different actual time as well as different ranges.
6. Using the simulation, adjust the angle until you find the maximum range for the given initial speed. Record all angle values attempted, and the ranges, in a neat table. Identify the angle that produced the maximum range.
|
Angle Attempted (degrees) |
Range (m) |
|
10 |
21.82 |
|
20 |
41 |
|
30 |
55.24 |
|
40 |
62.81 |
|
44 |
63.74 |
|
45 |
63.78 |
|
46 |
63.74 |
|
50 |
62.81 |
|
60 |
55.24 |
|
70 |
41 |
|
80 |
21.82 |
|
90 |
0.01 |
The angle that produces the maximum range is 45 0 . It gives a maximum range of 63.78m.
7. Finally, set the height to 20 m, and the launch angle to 0° while setting the initial velocity of 25 m/s.
a. Play the simulation and record the time and range.
b. How do you expect both the range and the time to change if you double the initial velocity to 50 m/s but leave all other settings the same? Explain.
I expect the range to double and the time will remain the same. For a projectile dropped from a height, the range doubles if the initial velocity is doubled. However, the time always remains constant unless the height is changed.
c. Play the simulation with the doubled velocity. Were your predictions correct? If not, why not?
Results obtained from the simulation proves that my prediction is accurate.
d. Compare your answers to step 3.
In part 3 when the initial velocity was doubled the ranged increased by 4 times while in part 7 when the initial speed was doubled the range also doubled. This is because the height of projectiles is different in the two steps.
Does doubling initial velocity always double the range of a projectile? Does it sometimes double the range? If so, under what circumstances?
Doubling the initial velocity does not always double the range of the projectile. However, it sometimes doubles the range but depends on the height of the projectile. If then the ranged increases by 4 times when the initial velocity is doubled. If
the range doubles if the initial velocity is doubled (but Ɵ>0).
e. Double the height to 40 m. Do you expect this change to double the range?
I expect the range to increase but not twice. As stated above, for a projectile dropped from a height, the range only doubles if the initial velocity is doubled.
f. Start the simulation. Did doubling the height double the range?
Doubling the height didn’t double the range.
