Key relationship
R=u²sin(2θ)/g.
Physics · Practical apparatus
Projectile range and protractor
Keep launch speed constant and sweep the protractor angle. Range peaks at 45° when launch and landing heights match. Complementary angles give equal ranges.
Open the interactive experiment →Projectile range and protractor
ஏவுதல் மற்றும் தரையிறங்குதல் ஒரே உயரத்தில் இருந்தால் 45°-இல் வீச்சு அதிகம். நிரப்பு கோணங்களின் வீச்சுகள் சமம்.
Key notes, relationships and model limits
Practical tip
Keep launch speed constant and sweep the protractor angle. Range peaks at 45° when launch and landing heights match. Complementary angles give equal ranges.
Common trap
The sin2θ range formula assumes equal launch and landing heights and no air drag; it is not valid for every launch.
Model limits
vacuum projectile, equal starting and landing heights; no drag or launch-speed variation.
What you will learn
Adjust projectile range and protractor apparatus, observe its reading and derive the indicated physical quantity.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
At u=20 m/s and g=9.81 m/s², 30° and 60° both give R≈35.31 m.
Why this matters
The model connects projectile range and protractor with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
Equal-speed projectiles at 30° and 60° have ranges that are?
- The 60° range is twice as large.
- Equal for equal launch and landing heights.
- The 30° range is twice as large.
Read the explanation
Equal for equal launch and landing heights.
Course connection: Virtual apparatus preparation. Check exact board/exam membership in the syllabus sources. Physical practical work remains necessary.