What it shows
The range of a projectile depends on the launch angle. On level ground and with little air drag, the greatest range occurs at 45 degrees, and complementary angles such as 30 and 60 degrees give the same range.
The science
Split the velocity into a horizontal part v cos(theta) and a vertical part v sin(theta). The vertical part decides how long the ball stays in the air, and the horizontal part decides how far it moves in that time. The range equals v squared times sin(2 theta) divided by g, and sin(2 theta) is largest for 45 degrees.
Materials
Cost: under Rs 50. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A wooden ruler and a rubber band to make a catapult
- A stand with a protractor to set angles
- Small soft balls or crumpled paper balls
- A long measuring tape
- Chalk and a notebook
- A friend to mark the landing
Safety
For this project: Launch only soft balls, away from people and windows. All others must stand behind the catapult and an adult must supervise.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Build a catapult by hinging one end of the ruler to a base and pulling it back with a rubber band to a fixed notch.
Fix the launch ramp to a protractor so that angles from 15 to 75 degrees can be set.
Mark a line on the ground at the launch point and extend the tape forward.
Launch the ball at 15 degrees with the same pull-back each time.
Mark where the ball first lands and measure the range.
Repeat each angle three times and use the average.
Do this for 15, 30, 45, 60 and 75 degrees.
Plot range against angle and find the peak and the pairs that give equal range.
What you should see
A bell-shaped graph with the longest range near 45 degrees, with 30 and 60 degrees giving similar ranges. Real data shows a slightly lower peak angle because of air drag.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1Which angle gives the maximum range on level ground?
45 degrees.
2Which two angles give equal range?
Any pair that adds to 90 degrees.
3Why keep the pull-back the same?
To keep the launch speed constant.
4What changes if air drag is large?
The best angle becomes a little less than 45 degrees.
Take it further
Launch from a table and test whether the best angle goes below 45 degrees.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
Free ebooks for this project
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