Edexcel 2024 Paper 3 Question 5 Solution

Edexcel 2024 Paper 3 Question 5 – Projectile Motion Explained

❓ The Question

💡 Teacher Explanation

There’s nothing especially new here. It’s standard projectile motion, just spread across a few parts.

The key thing is keeping it organised. First you resolve the velocity, then write the equations, then remove $t$ . That middle step matters more than people expect. If it’s messy, the rest becomes harder.

After that, you’re really just working with a quadratic. Some students spot that and use it well. Others don’t, and end up doing more work than they need to.

🎯 How To Recognise This Question Type

Angle + speed → resolve → write $x$ , $y$ → eliminate $t$

🧠 Step By Step Solution

Step 1: Resolve velocity

Given $\tan\alpha = \frac{3}{4}$ , use a triangle.

So:

$\sin\alpha = \frac{3}{5}$
$\cos\alpha = \frac{4}{5}$

That gives:

Horizontal = $28$
Vertical = $21$

Step 2: Write equations

Horizontal:
$x = 28t$

Vertical:
$y = 21t - 4.9t^2$

Nothing complicated here. Just standard setup.

Step 3: Eliminate $t$

From $x = 28t$ :
$t = \frac{x}{28}$

Substitute into $y$ :

$y = 21\left(\frac{x}{28}\right) – 4.9\left(\frac{x}{28}\right)^2$

Take your time simplifying this. It’s where most small errors happen.

You should end up with:
$y = \frac{3}{4}x – \frac{1}{160}x^2$

Step 4: Find the range

Set $y = 0$ :

$0 = \frac{3}{4}x – \frac{1}{160}x^2$

Solve:

$x = 120$

Step 5: Maximum height

You could differentiate, but here it’s easier to use symmetry.

Half the range:
$x = 60$

Substitute:

$y = 22.5$

Step 6: Compare heights

Air resistance slows the particle more quickly, so it doesn’t go as high.

So:
$H > K$

Step 7: Limitation

The model is still simplified. For example:

assumes constant $g$
doesn’t properly model air resistance

✅ Final Answer

(a) $y = \frac{3}{4}x – \frac{1}{160}x^2$
(b) $120 \text{ m}$
(c) $22.5 \text{ m}$
(d) $H > K$
(e) ignores real air resistance effects

✔ This would score full marks

🎯 Mark Scheme Breakdown

This one is mostly about method. If the working is there, the marks tend to follow. If it isn’t, even a correct answer doesn’t help much.

(a) Equation of the path (6 marks)

M1:
Uses horizontal motion, something like $x = 35\cos\alpha , t$ seen
A1:
Correct expression for $x$ after resolving
M1:
Uses vertical motion, e.g. $y = 35\sin\alpha , t – \frac{1}{2}gt^2$ seen
A1:
Correct expression for $y$
DM1:
Time is removed properly
You need to actually substitute — it has to be visible in the working
A1*:
Final equation
$y = \frac{3}{4}x – \frac{1}{160}x^2$ seen exactly

Important point here — if you just write that equation down, you don’t get the marks. It has to be built.

(b) Range (2 marks)

M1:
Some clear method — usually setting $y = 0$
A1:
$120 \text{ m}$ seen

Doesn’t matter how you do it, but it needs to be shown.

(c) Maximum height (2 marks)

M1:
Valid approach — midpoint, differentiation, or suvat all fine
A1:
$22.5 \text{ m}$ seen
(accept $23$ )

A lot of people use the midpoint here, which is quicker.

(d) Comparison (1 mark)

B1:
Statement that $H > K$ seen

Needs a reason linked to air resistance. Just writing the inequality isn’t always enough on its own.

(e) Limitation (1 mark)

B1:
One sensible limitation seen

For example, assuming constant $g$ or not modelling air resistance properly.

What tends to go wrong

Jumping straight to the equation in (a) with no working
Not clearly substituting when removing $t$
Small algebra mistakes that carry through
Overthinking (b) and (c)
Being too vague in the last two parts

What still gets credit

Method marks are usually safe if the structure is there
Follow-through works — you can still pick up marks after a mistake
Different valid approaches are accepted, especially in (b) and (c)

Total: 12 marks

⚠️ Examiner Insight

Most students were fine at the start. The setup was usually done correctly.

The main issues came when things were rushed. Some answers jumped straight to the final equation without showing how it was formed, which loses all the marks for that part. Others made small algebra mistakes and didn’t catch them.

In the middle of the question, some didn’t recognise how useful the shape of the graph is. That meant more work and more chances to go wrong.

The final parts weren’t difficult, but answers were often too vague. That’s where marks quietly disappeared.

💬 Need help with questions like this?

If these longer questions are where things tend to break down, it’s usually about structure rather than difficulty.
Working with an online maths tutor for A Level can help you organise your method and avoid dropping marks late in questions.

🔗 Next Steps

← Question 4 Solution
→ Question 6 Solution

👨‍🏫Author Bio

S Mahandru is an A Level Maths specialist who focuses on helping students improve exam technique and handle multi-step questions more confidently under pressure.

❓ Frequently Asked Questions

📌 Why do we eliminate t?

Because the final equation needs to link $x$ and $y$ directly. Time is only used as a step in between. If you leave it in, you don’t get the required form.

📌Do I have to use symmetry for the maximum height?

No, you can differentiate instead. But symmetry is quicker here and reduces the chance of making a mistake.

📌Why is quoting the equation not allowed?

Because the question says “show that”. The marks are for the method, not just the final result. If you skip the working, you lose those marks.

📌 What is the most common mistake in this question?

Usually it’s rushing the algebra when eliminating $t$ . A small slip there affects everything that follows, even if the setup was correct.