Can you solve it? Physics
Ten problems that get harder as you go. Each has a hint and a full worked solution, but try properly before you look. Your progress is saved on this device.
- 1Hard
The busy fly
Two trains start 100 km apart on the same track and head towards each other, each at 50 km/h. A fly starts on the front of one train and flies at 75 km/h to the other, turns instantly, flies back, and keeps going until the trains meet. How far does the fly travel in total?
- 2Very hard
The last 35 metres
A stone is dropped from the top of an 80 m tower. Ignore air resistance and take g = 10 m/s². How long does it take to fall the last 35 m?
- 3Fiendish
The stone in the ice
An ice cube with a small stone frozen inside floats in a glass of water. When the ice melts and the stone sinks to the bottom, what happens to the water level?
- 4Hard
Heavier in the lift
A 50 kg student stands on bathroom scales in a lift that is accelerating upwards at 2 m/s². Take g = 10 m/s². What force do the scales show, in newtons?
- 5Very hard
Off the cliff
A ball is kicked horizontally at 15 m/s off a cliff 20 m high. Take g = 10 m/s² and ignore air. How far from the foot of the cliff does it land?
- 6Very hard
The smallest mirror
Priya is 1.6 m tall and stands in front of a flat wall mirror. What is the shortest mirror (in metres) that lets her see her whole body from head to toe?
- 7Very hard
Ramp then rough floor
A 2 kg block slides from rest down a frictionless ramp from a height of 5 m, then along a rough horizontal floor where the coefficient of friction is 0.25. How far along the floor does it slide before stopping?
- 8Fiendish
A clock on the Moon
A pendulum takes 2 s for one complete swing on Earth. The Moon's gravity is one sixth of Earth's. How long does one swing take on the Moon?
- 9FiendishLong problem
The cannon on the cliff
A cannon on top of a 45 m cliff fires a ball at 40 m/s, aimed 30° above the horizontal, out over flat ground. Take g = 10 m/s² and ignore air resistance. Work through all four parts, then type your answer to part (d).
Equation sheet Launch speed u = 40 m/s, angle θ = 30°, cliff height h = 45 m, g = 10 m/s²uₓ = u cos θ = 40 × cos 30° = 40 × (√3 / 2) = 20√3 ≈ 34.64 m/su_y = u sin θ = 40 × sin 30° = 40 × ½ = 20 m/sHorizontal: x(t) = uₓ t (no force sideways, so uₓ never changes)Vertical: y(t) = h + u_y t − ½ g t² (height above the ground) v_y(t) = u_y − g tAt the top of the flight: v_y = 0On landing: y(t) = 0 ⟹ h + u_y t − ½ g t² = 0Quadratic formula: t = [ −b ± √(b² − 4ac) ] / 2aImpact speed: v = √( uₓ² + v_y² )- (a) How long after firing does the ball reach its highest point?
- (b) How high above the ground is it at that moment?
- (c) How long is the ball in the air altogether?
- (d) How far from the foot of the cliff does it land? Give your answer to 1 decimal place.
- 10FiendishLong problem
Two batteries, three wires
A circuit has two branches joined at a top junction X and a bottom junction Y. The left branch has a 12 V battery and a 2 Ω resistor; the right branch has a 6 V battery and a 3 Ω resistor; a middle branch has a single 6 Ω resistor. Both batteries have their positive terminal towards X. Use Kirchhoff's laws to find the current in every branch, then type the current through the 6 Ω resistor.
Equation sheet Unknowns: I₁ = current up through the 12 V branch, I₂ = current up through the 6 V branch, I₃ = current down through the 6 Ω middle resistorKirchhoff's current law at X: current in = current out I₁ + I₂ = I₃ (1)Kirchhoff's voltage law: round any closed loop, Σ(emf) = Σ(I R)Left loop (12 V battery, 2 Ω, then down through 6 Ω): 12 = 2 I₁ + 6 I₃ (2)Right loop (6 V battery, 3 Ω, then down through 6 Ω): 6 = 3 I₂ + 6 I₃ (3)Power in a resistor: P = I² R- (a) Use (2) and (3) to write I₁ and I₂ in terms of I₃.
- (b) Substitute into (1) and solve for I₃.
- (c) Find I₁ and I₂. Which way does the current really flow through the 6 V battery?
- (d) Type the current through the 6 Ω resistor in amps, to 2 decimal places.