Question

Мяч бросают с высоты 10 м вертикально вниз со скоростью 10 м/с. Найти скорость мяча на высоте 2 м. ДАЮ 100 БАЛОВ!!

Answer 1

По закону сохранения енергии: потенциальная энергия мяча на высоте 10 м равна кинетической энергии мяча на высоте 2 м.

$\tt \dfrac{mv^2}{2}=mgh$

$\tt v=\sqrt{2gh}=\sqrt{2\cdot 10\cdot (10-2)}\approx 12.6$ км/ч

Answer 2

Problem Analysis

We are given the following information: - The ball is thrown vertically downwards from a height of 10 m. - The initial velocity of the ball is 10 m/s.

We need to find the velocity of the ball when it is at a height of 2 m.

Solution

To solve this problem, we can use the equations of motion for uniformly accelerated motion. Since the ball is thrown vertically downwards, we can consider the acceleration due to gravity as the acceleration.

The equations of motion for uniformly accelerated motion are:

1. Final velocity (v) = Initial velocity (u) + Acceleration (a) * Time (t) 2. Displacement (s) = Initial velocity (u) * Time (t) + 0.5 * Acceleration (a) * Time (t)^2 3. Final velocity squared (v^2) = Initial velocity squared (u^2) + 2 * Acceleration (a) * Displacement (s)

In this case, the initial velocity (u) is 10 m/s, the acceleration (a) is -9.8 m/s^2 (negative because it is acting downwards), and the displacement (s) is 10 m - 2 m = 8 m (since the ball is at a height of 2 m from the starting point).

We can use equation 3 to find the final velocity squared (v^2) and then take the square root to find the final velocity (v) at a height of 2 m.

Calculation

Let's calculate the final velocity (v) at a height of 2 m.

Using equation 3: v^2 = u^2 + 2 * a * s v^2 = (10 m/s)^2 + 2 * (-9.8 m/s^2) * 8 m v^2 = 100 m^2/s^2 - 156.8 m^2/s^2 v^2 = -56.8 m^2/s^2

Since velocity cannot be negative in this context, we can ignore the negative sign.

Taking the square root of both sides: v = √(56.8 m^2/s^2) v ≈ 7.54 m/s

Answer

The velocity of the ball at a height of 2 m is approximately 7.54 m/s.

Please note that the above calculation assumes no air resistance and neglects any other external factors that may affect the motion of the ball.