Reach for the Summit problem set - Physics

Welcome to the road to Olympics! By this problem set, you will lead your way to the summit of physics, just like climbing mountain in Celeste.

To match the Celeste scheme, each section will be seperated into A,B,C sides, each of which has lots of problems, having the similar format. The difficulty of the problems may be randomly shuffled, though.

I'll use this problem set for my games or programs later on, and I will upgrade it frequently.

Problem Format: For example, if the problem is on Stage 1, A side and 5th position, then the name of the problem will be:

Reach for the Summit - P-S1-A5

Table of Contents:

Stage 1: Kinematics

Stage 2: Equilibrium of Objects

Stage 3: Newton's Laws of Motion, Inertia

Stage 4: Centey of Mass, Momentum and Angular Momentum

Stage 5: Energy

Stage 6: Vibration and Wave

Stage 7: Thermodynamics

Stage 8: Electrostatic Field

Stage 9: Constant Currents

Stage 10: Magnetic Field and Induction

Stage 11: Alternating Current and Electromagnetic Wave

Stage 12: Optics

Stage 13: Modern Physics

Note by Alice Smith
3 months, 1 week ago

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Reach for the Summit - P-S1-A1

A UFO is moving at a constant velocity vv from OO along ray OBOB, and OAOA is horizontal, as shown in the picture. Alice is observing it at point AA, and BOA=θ\angle BOA = \theta, which can be considered constant during the observation.

Given that the UFO is giving off a small pulse of sound wave and then a big pulse after τ (τ0)\tau\ (\tau \rightarrow 0) seconds.

If OA=LOA=L, and the speed of sound in the air is vv', at what condition for vv can Alice record the big pulse first and then the small pulse of sound wave?

Take θ=30°\theta = 30 \degree, and the condition is v>λvv > \lambda v'. Submit 1000λ\lfloor 1000\lambda \rfloor.

Alice Smith - 3 months, 1 week ago

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Reach for the Summit - P-S1-A2

As shown above, a rod with length ll is leaning against the vertical wall. The lowest point of the rod, AA is moving right at velocity v0v_0, at this time, the angle of the rod and the ground is α\alpha.

Then there exists a point on the rod which has the minimum magnitude of velocity. Find the minimum velocity.

Take α=30°\alpha=30 \degree, and the minimul velocity is λv0\lambda v_0. Submit 10000λ\lfloor 10000 \lambda \rfloor.

Alice Smith - 3 months, 1 week ago

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Reach for the Summit - P-S1-A3

As shown above, the point OO is H mH\ m away from the ground. Two balls 1,21,2 are thrown at point OO horizontally, so that ball 11 merely passes the top of the fence and falls at point BB, ball 22 is bounced by the ground once and then merely passes the top of the fence and falls at point BB.

If the collision of ball 22 and ground is elastic, find the height of the fence h (m)h\ (m).

The result is h=λHh=\lambda H, submit 1000λ\lfloor 1000\lambda \rfloor.

Alice Smith - 3 months, 1 week ago

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Reach for the Summit - P-S1-A4

A pipe with diameter D=0.2 mD=0.2\ m is put on the horizontal ground, and Ant-Man wants to jump over it to practice his strength.

If Ant-Man is initially on the ground, and he can start to jump anywhere, what's the minimum initial velocity he should have to jump over the pipe?

Let vmv_m be the minimum velocity (m/s)m/s). Submit 1000vm\lfloor 1000v_m \rfloor.

Assumptions:

  • Ignore air resistance.

  • He can be treated as a mass point.

  • Take gravitational acceleration g=10m/s2g=10 m/s^2.

Alice Smith - 3 months, 1 week ago

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Reach for the Summit - P-S1-A5

As shown above, AB,BC,CD,ADAB,BC,CD,AD are four rigid rods connected by hinges whose lengths are LL, and it's obvious that quadrilateral ABCDABCD is a rhombus.

Initially, the diagonal BDBD is longer than ACAC, and the rhombus is put on the horizontal ground, then A,CA,C is moving to the opposite side along line ACAC with the same magnitude of velocity vv.

What's the acceleration (m/s2)(m/s^2) of point BB relative to the ground at the moment when the rhombus becomes a square (see the picture on the right)?

Submit the value when L=2 m, v=10 m/sL=\sqrt{2}\ m,\ v=10\ m/s.

Alice Smith - 3 months, 1 week ago

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