Question

+50 БАЛЛОВ!!!! СРОЧНО!!! Мяч, брошенный вертикально вверх со скоростью 12 м/c, упал на Землю через 3 с. Определите высоту подъема мяча и его скорость перед ударом о землю.

Answer 1

Закон сохранения энергии: кинетическая энергия мяча в начальной точке равна его потенциальной энергии в наивысшей точке.
Кинетическая энергия мяча = 0,5*M*V^2= M*144*0,5= 72M
здесь V - скорость мяча
M - масса мяча
Потенциальная энергия мяча = Mgh= М*9,8*h
g = 9,8 m/сек^2 - ускорение свободного падения
h - высота подъема мяча

Mgh = 0,5M V^2 отсюда 72М = М*9,8h

h = 72/9,8 = 7,35 м/сек

Скорость мяча перед ударом о землю равна его начальной скорости 12 м/сек.
(Зачем дано дополнительное условие 3 сек - я не очень понял. Разве что мяч кидают не на Земле?)

Answer 2

Calculation of the Ball's Maximum Height and Velocity

To determine the maximum height reached by the ball and its velocity just before hitting the ground, we can use the equations of motion.

Let's denote the initial velocity of the ball as v₀ (which is 12 m/s in this case) and the time it takes for the ball to fall back to the ground as t (which is 3 seconds in this case). We need to find the maximum height (h) and the velocity just before hitting the ground (v).

The equation for the maximum height reached by an object thrown vertically upward is given by:

h = (v₀²)/(2g)

where g is the acceleration due to gravity (approximately 9.8 m/s²).

Using this equation, we can calculate the maximum height as follows:

h = (12²)/(2 * 9.8)

Now, let's calculate the value of h:

h = (144)/(19.6) ≈ 7.35 meters

Therefore, the maximum height reached by the ball is approximately 7.35 meters.

To find the velocity just before hitting the ground, we can use the equation:

v = v₀ + gt

where v₀ is the initial velocity, g is the acceleration due to gravity, and t is the time taken to fall back to the ground.

Using this equation, we can calculate the velocity just before hitting the ground as follows:

v = 12 + (9.8 * 3)

Now, let's calculate the value of v:

v = 12 + 29.4 = 41.4 m/s

Therefore, the velocity of the ball just before hitting the ground is approximately 41.4 m/s.

Please note that these calculations assume no air resistance and a constant acceleration due to gravity.