# 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

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 weeks, 4 days ago

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A UFO is moving at a constant velocity $v$ from $O$ along ray $OB$, and $OA$ is horizontal, as shown in the picture. Alice is observing it at point $A$, and $\angle BOA = \theta$, 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 $\tau\ (\tau \rightarrow 0)$ seconds.

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

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

- 3 weeks, 4 days ago

As shown above, a rod with length $l$ is leaning against the vertical wall. The lowest point of the rod, $A$ is moving right at velocity $v_0$, at this time, the angle of the rod and the ground is $\alpha$.

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

Take $\alpha=30 \degree$, and the minimul velocity is $\lambda v_0$. Submit $\lfloor 10000 \lambda \rfloor$.

- 3 weeks, 4 days ago

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

If the collision of ball $2$ and ground is elastic, find the height of the fence $h\ (m)$.

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

- 3 weeks, 1 day ago

A pipe with diameter $D=0.2\ m$ 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 $v_m$ be the minimum velocity ($m/s)$. Submit $\lfloor 1000v_m \rfloor$.

Assumptions:

• Ignore air resistance.

• He can be treated as a mass point.

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

- 3 weeks, 1 day ago

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

Initially, the diagonal $BD$ is longer than $AC$, and the rhombus is put on the horizontal ground, then $A,C$ is moving to the opposite side along line $AC$ with the same magnitude of velocity $v$.

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

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

- 3 weeks, 1 day ago