Physics IA · A · Space, time and motion · topic 1 of 30
Projectile: is the best launch angle really 45°? · IB Physics IA idea: guide, sample graph and step-by-step plan
a famous rule: test where it breaksEveryone knows 45° gives the longest throw. That is only true on level ground. You're going to find out where it stops being true.
- ✓ you like testing a famous rule
- ✓ you can set up a repeatable launcher
- ✓ you enjoy a bit of algebra
The big idea
← the height is your twist!With no air resistance and launch from ground level, range is R = v² sin 2θ / g, longest at 45°. Launch from a height h and the best angle moves below 45°, because the ball has extra time in the air to use. The shape of the whole range-angle curve is the test. Measure range for a spread of angles, find where yours peaks, and compare with the prediction. Controlling the launch speed is what makes or breaks this IA.
Make it yours: pick one twist
Copying a classic won't show your choices. Pick one of these (or invent your own) and your IA becomes yours.
Swipe for more twists →
Repeat the angle series from two or three heights.
→ The best angle should shift as h grows; your conclusion compares peak positions, not just one curve.Aim at a floor lower than the launcher, as in a throw off a balcony.
→ Same equations with a new h; the effect is bigger, so the shift in best angle is easier to see.Fire horizontally from a table and get v from the range and fall time, then reuse that v.
→ Gives you a measured v for the model line rather than a guess, and the evaluation compares two methods.Use a light ball or a larger launch speed and compare with the drag-free model.
→ Peak angle and range drop below the model; needs an extra theory section, so stretch.Film the flight and fit the trajectory instead of reading the landing point.
→ Gives you speed and angle from the data; your graph becomes y against x.A basketball free throw, a cricket throw, or a water jet.
→ Gives the introduction a purpose; the physics and graph stay the same.Your Physics IA research question: run the check
Write your own question first. Then make sure it ticks every box:
- Names one independent variable and its range (which angles, how many, at what height).
- Names one dependent variable and how it is measured (range from where to where, how marked).
- Says what stays fixed (launch speed and how you check it, launch height, the ball).
- Says what you compare with (the drag-free range formula, or the best angle it predicts).
- Is narrow enough for about 10 hours, with at least 7 angles and repeats at each.
The set-up
One way to arrange it. Draw yours with the real launch height and the angle scale you use.
How your Physics IA could be laid out
The usual order for a topic like this, what each part needs to show, and roughly how much of your 3,000 words it takes. The words are all yours.
Your question; where launch angle matters (sport, water jets); what you expect and why.
Independent horizontal and vertical motion; range formula at ground level and from a height; why the best angle changes; assumptions such as no drag.
Independent, dependent and controlled variables, each with how you set, measure or hold it, and why it matters.
How the launcher is clamped and its angle set; how launch speed is kept constant and checked; how landing points are marked and measured; repeats.
Short and specific: moving ball, eye protection, clear landing zone.
One table: angle, each range reading, units and uncertainties in the headers.
Averaging repeats, the uncertainty in range and angle, and how you find the best angle from your curve.
Range against angle with the model curve(s) and error bars; how you located the peak and its uncertainty.
Answer with numbers: where your peak is, how it compares with the model, and the effect of height.
Weaknesses ranked by their effect on your result, each linked to a realistic improvement.
Every source for theory and method.
What your Physics IA graph could look like
model curves AND data ✓Made-up data, to show you the form of a strong graph, not the answer. Yours will look different. example only
- Both model curves are drawn so the reader can see which one your data follows.
- Error bars on both axes. The range bars come from the spread of repeat shots, which is usually far bigger than the ruler's resolution.
- The peak is broad, so point to a region and not a single angle, and say how you chose it.
- Check the axes: starting at zero shows the ground-level curve and the shape of the model.
- Another graph to consider: R against sin 2θ for the floor-level case, which should be a straight line if the model holds.
Which uncertainty matters most?
Rank by the effect on your result, here the range at one angle. Notice what matters near the peak, and what does not.
Your game plan
test the launcher first!Tick steps off as you go. We'll remember on this device.
0 of 11 done
- Read and predictDerive or find the range formula for ground-level launch and for launch from a height. Predict the best angle for your height before you measure anything.
- Trial run (1 lesson)Fire a few shots at one angle. How much does the landing point scatter? Does the launcher slip? Fix the problems now.
- Test the launcherFire ten shots at one angle and look at the spread. If the spread is large, fix the launch before you collect anything else.
- Decide range, repeats and markingChoose at least 7 angles, how many shots each, and how you mark and read the landing point (carbon paper, not by eye).
- Collect the dataRecord raw readings in the table with units and the resolution of the ruler and protractor. Note odd shots.
- ProcessAverage the repeats, carry the uncertainty on range and angle through, and say how you treat outliers.
- Graph and fitPlot range against angle with error bars. Draw the model curve and decide how you locate the peak and its uncertainty.
- Compare with theoryWhere is the best angle, and is it below 45°? Does the model need a launch speed that you measured independently?
- EvaluateRank the weaknesses by effect on your result. Make each improvement specific to a weakness you found.
- Write, then cutWrite in the order of the layout and stay within 3,000 words. Tables, graphs and references do not count.
- Check before your teacher's draftRun through the checklist below, then get your RQ or draft checked. Your teacher reads one draft only.
Physics you'll need
Traps to avoid in this Physics IA
- An inconsistent launch speed that you never measured, then blaming the scatter on the ball.
- Reading landing points by eye instead of marking them.
- Taking the best angle as the highest of seven points rather than finding the peak of a curve.
- Measuring range from the wrong zero (launcher base rather than the muzzle).
- A launcher that slips or whose angle changes as the spring loads.
- Ignoring that the muzzle is not at floor level when comparing with v² sin 2θ / g.
- Using the ground-level formula without saying why your set-up is different.
More Physics IA ideas like this
- Friction: is the coefficient really a constant?●●○
- Paper cones: what sets the terminal speed?●●○
- Trolley on a ramp: how much energy does friction take?●●○
This guide shows how a topic like this is usually approached. It is not an IA. Your question, choices, data, analysis and words must be your own: change something, tell your teacher where the idea came from, and follow your school's rules on outside help.