Question 1. A boy wants to build a bamboo raft. He knows that he needs 50 whole bamboo stems, each at least 2 bu long (an ancient Chinese unit of length, approximately equal to 1.67 m). He goes to a freshly cut bamboo grove and waits for the new bamboo to grow. It is known that bamboo grows 6.68 cm per day, and there are 75 bamboo plants in the grove. How long will the boy have to wait?

Question 2. A train crossed a bridge of length $L = 400$ m in $t_1 = 24$ seconds. A guard standing on the bridge observed that the train was passing by him for $t_2 = 16$ seconds. How long was the train driver on the bridge?

Question 3. A tracked tractor is moving at a speed of $v = 20$ km/h. At what speed are the top tracks of the tractor moving?

Question 4. Determine the volume of your body and express it in liters. Estimate the uncertainty of your result.

Question 5. An ice cube containing a frozen metal washer is floating in a glass of water. How will the water level in the glass change when the ice cube melts? Provide a detailed explanation of your answer. You can neglect water evaporation and thermal expansion of water.

Question 6. Two identical balls are moving with the same speed in the same direction across a smooth surface. One ball encounters a small dip, while the other encounters a bump of the same shape. The balls reach the obstacles simultaneously. Will either ball overtake the other after passing the obstacle?

Question 7. There is no snow in Sydney. In which month do the power lines in the vicinity of Sydney sag the lowest?

Question 1. Peter is hammering nails with a hammer whose working part has a mass of $m = 1.2$ kg. 40% of the hammer's energy is converted into heat, and in 1 minute, the working part's temperature increases by 4°C, while the nails remain unheated. After working for two minutes, Peter gets tired. How much work did Peter perform in hammering nails with the hammer? What power did he generate? Assume the specific heat capacity of the hammer's working material is $C = 500$ J/(kg·K).

Question 2. A pot containing 1 liter of water cannot be brought to a boil using a heater with a power of 100 W. How long will it take for the water to cool by 1°C if the heater is turned off after attempting to boil it?

Question 3. On a cold, rainy October day, Grandma Ann did a large load of laundry. However, the laundry dries slowly in a small room despite central heating. Will the laundry dry faster if Grandma Ann opens the window? Provide a detailed explanation of your answer.

Question 4. The power line of a small workshop runs through Grandma Ann's garden. The line operates at 220 V, and the current is alternating. The workshop consumes 100 kW of electrical power. One night, Grandma Ann decided to light up her yard for free and cut one wire of the line, connecting a 100 W light bulb to the exposed contacts. What will happen when the machines are turned on in the morning?

Question 5. Kolya Bulkin is looking at a fountain and sees a coin at the bottom. His vision, accustomed to air, estimates the distance to the coin as 40 cm. Can he reach the coin if his arm is 55 cm long and he does not want to get anything else wet?

Question 6. A fiber optic cable is a long, thin, straight cylindrical thread made of glass with a refractive index of $n = 1.23$. A light source is pressed against one end of the cable, and the other end is $L = 10$ cm away from a screen. Estimate the diameter of the light spot on the screen.

Question 7. Determine the volume of your body and express it in liters. Estimate the uncertainty of your result.

Question 1. Kolya Bulkin wants to swim across a river with a current speed of 6 km/h. Unfortunately, he can swim at a speed of only 3 km/h. At what angle to the riverbank should he swim to minimize the drift?

Question 2. A fly is flying horizontally at a speed of $v$. Suddenly, it notices a drop of jam directly below it at a vertical distance of $H$. Using its wings, the fly can accelerate itself with a magnitude of $a$ in any direction completely ignoring gravity. What is the minimum time it can reach the drop of jam? Provide a detailed explanation of the optimal trajectory.

Question 3. A duck is flying horizontally at a speed of $u$ above a hunter. The inexperienced hunter throws a stone at the duck, aiming such that, at the moment of the throw, the stone's velocity is directed at the duck's current position. The angle between the stone's initial velocity and the horizontal is $\alpha$. At what height was the duck flying if the stone hit it?

Question 4. Can the distance traveled by a particle during the last second of uniformly accelerated motion be equal to the distance traveled by the same particle during the second-to-last second?

Question 5. A bag of mass $M = 30$ kg lies on a rough horizontal floor. The coefficient of friction between the floor and the bag is $\mu = 0.1$. Find the minimum force required to move the bag from rest.

Question 6. A sandbag of mass $M = 50$ kg falls from a height $H = 1$ m onto the right end of a weightless, perfectly rigid, horizontal seesaw. The distance from the point of impact to the seesaw's fulcrum is $L = 3$ m. On the other end of the seesaw, at a distance $l = 1$ m from the fulcrum, sits a girl of mass $m = 50$ kg. To what height will the girl rise? Neglect the size of the girl and the sandbag.