Question

Минутная стрелка часов в 3раза длинее секундной. Найти отношение линейной скорости конца минутной стрелки к линейной скорости конца секундной стрелки.

Answer 1

Секундная  стрелка  делает  1  оборот  за 60  секунд. Пусть длинна  секундной стрелки  равна L(м) . То  ее   конец   описывает  окружность  длинны  S1=2*pi*L(м)
То  ее  линейная скорость: V1=S1/t=2*pi*L/60с=pi*L/30 (м/с)
Длинна  минутной   равна 3L.  Она описывает   окружность  длинны :S2=6*pi*L
Минутная стрелка  делает 1  оборот  за 3600 секунд. То  ее линейная скорость:  V2=6*pi*L/3600c=pi*L/600 (м/с)
Отношение скорости  минутной к  секундной:
V2/V1=pi*L/600 /(pi*L/30)=30/600=1/20=0,05
Ответ:0,05

Answer 2

Calculation of the Linear Velocity Ratio

To find the ratio of the linear velocity of the minute hand to the linear velocity of the second hand, we need to consider the relationship between the lengths of the two hands.

Given that the minute hand is three times longer than the second hand, we can denote the length of the second hand as L and the length of the minute hand as 3L.

The linear velocity of an object is defined as the distance traveled per unit time. In this case, we can consider the linear velocity at the end of each hand.

The linear velocity of the second hand can be denoted as v2, and the linear velocity of the minute hand can be denoted as v3.

To find the ratio of the linear velocities, we can use the formula:

v3 / v2 = (3L) / L = 3

Therefore, the ratio of the linear velocity of the minute hand to the linear velocity of the second hand is 3.

Please note that the above calculation assumes that the rotation of the clock hands is uniform and that the hands move at a constant speed. Additionally, this calculation does not take into account any external factors that may affect the movement of the clock hands.