Problems from Oct 13, 2026

All 12 problems from Oct 13, 2026, across Physics, Math, Chemistry, Electrical engineering. Try each one first, then check the answer and the main steps below.

Physics

Problem 1: Counting to the thunder

You see a flash of lightning and hear the thunder $6\ \text{s}$ later. Light arrives almost instantly. Sound travels at $340\ \text{m/s}$.

How far away did the lightning strike?

Answer: 2040 m

How it is solved

  1. Light is instant, sound is not: The delay is the time the sound took to travel.
  2. Distance = speed × time: $340 \times 6$. ($2040\ \text{m}$)

Problem 2: A loading ramp

A ramp is 8 m long. It slopes at $30^\circ$ to the ground. For a $30^\circ$ slope, the height gained is $0.5$ times the length along the slope.

How high does it lift something that travels its full length, in metres?

Answer: 4 m

How it is solved

  1. Height = 0.5 × length: $4\ \text{m}$

Problem 3: Trolleys that stick

A $2$ kg trolley moving at $6$ m/s hits a $4$ kg trolley at rest. They stick together.

How fast do they move together just after they stick?

Answer: 2 m/s

How it is solved

  1. Momentum is conserved
  2. Before: $12$
  3. After: $v = 2\ \text{m/s}$

Math

Problem 1: Three in a row

The sum of three consecutive whole numbers is $114$.

What is the largest of the numbers?

Answer: 39

How it is solved

  1. Use the middle: The numbers are evenly spaced, so their mean is the middle one: $114 \div 3$. (mean $38$)
  2. Walk up to the largest: The gap between numbers is $1$. The largest is $1$ gaps above the middle. ($38 + 1 = 39$)

Problem 2: Savings

A savings account pays 4% simple interest each year on 500 dollars. The money stays in the account for 3 years.

How much is in the account at the end, in dollars?

Answer: 560

How it is solved

  1. Find the interest: $\char"24 60$
  2. Add it to the start: $\char"24 560$

Problem 3: Standing in a line

$5$ friends line up for a photo.

In how many different orders can they be arranged if two particular ones, Ana and Bo, must be next to each other?

Answer: 48

How it is solved

  1. Glue the pair together
  2. Arrange the things: $24$
  3. Count the block's own order: $24 \times 2 = 48$

Chemistry

Problem 1: Moles of water

Atomic masses: H $=1$, O $=16$.

How many moles are in $36\ \text{g}$ of $\ce{H2O}$?

Answer: 2 mol

How it is solved

  1. Find the molar mass: Add the atomic masses in $\ce{H2O}$. ($18\ \text{g/mol}$)
  2. Moles = grams ÷ molar mass: $36 \div 18$. ($2\ \text{mol}$)

Problem 2: A gas under a piston

A gas is under a piston at the conditions shown. The temperature stays the same and the pressure is raised to $2$ atm.

What is the new volume, in litres? (Pressure times volume stays the same.)

Answer: 11.2

How it is solved

  1. Read the starting volume: $22.4\ \text{L}$
  2. Pressure × volume stays the same: $11.2\ \text{L}$

Problem 3: A lime kiln

The reaction is $\ce{CaCO3 -> CaO + CO2}$. Atomic masses: Ca $=40$, C $=12$, O $=16$.

A student starts with $50\ \text{g}$ of $\ce{CaCO3}$ and collects $21\ \text{g}$ of $\ce{CaO}$.

What is the percent yield?

Answer: 75

How it is solved

  1. Moles of the starting material: $0.5\ \text{mol}$
  2. The most that could form: $28\ \text{g}$ (theoretical)
  3. Compare with what was collected: $75\%$

Electrical engineering

Problem 1: A light bulb for a month

A $60$ W bulb is on for $5$ hours a day for $30$ days. Electricity costs $\char"24 0.15$ per kilowatt-hour.

What does it cost, in dollars?

Answer: 1.35

How it is solved

  1. Power in kilowatts: $60\ \text{W} = 0.06\ \text{kW}$.
  2. Energy used: $0.06 \times 5 \times 30$. ($9\ \text{kWh}$)
  3. Cost: $9 \times 0.15$. ($\char"24 1.35$)

Problem 2: Choosing an input

The picture shows a logic circuit with the inputs set: A = 1, B = 0, S = 0.

What is the value of the output Y? (Answer 0 or 1.)

Answer: 1

How it is solved

  1. Gate N1 (NOT): $1$
  2. Gate G1 (AND): $1$
  3. Gate G2 (AND): $0$
  4. Gate Y (OR): $1$

Problem 3: A divider with a load

A $12$ V battery feeds a $1000$ ohm resistor in series with a $1000$ ohm resistor. A $1000$ ohm load is connected across the second resistor.

What voltage is across the load?

Answer: 4 V

How it is solved

  1. Combine the second resistor and the load: $500\ \Omega$
  2. Now it is a simple divider: $0.333333$ of the battery
  3. Voltage across the load: $4\ \text{V}$