Question

з балкона кинули м'яч вертикально вгору з початковою швидкістю 5 м/с. Через 2 с м'яч упав на землю. Визначити висоту балкона над землею і швидкість м'яча в мемент удару об землю​

Answer 1

Відповідь:

Пояснення:

дано

v=5m/c

t=2c

g=10m/c²

h-?

$h=v0t+\frac{gt^{2} }{2} =5*2+\frac{10*2^{2} }{2} =10+20=30m$

Answer 2

Problem Analysis

We are given that a ball is thrown vertically upwards from a balcony with an initial velocity of 5 m/s. After 2 seconds, the ball falls back to the ground. We need to determine the height of the balcony above the ground and the velocity of the ball at the moment it hits the ground.

Calculation of the Height of the Balcony

To calculate the height of the balcony above the ground, we can use the equation for the vertical displacement of an object in free fall:

Δy = v₀t + (1/2)gt²

Where: - Δy is the vertical displacement (height) - v₀ is the initial velocity - t is the time - g is the acceleration due to gravity (approximately 9.8 m/s²)

Substituting the given values into the equation, we have:

Δy = (5 m/s)(2 s) + (1/2)(9.8 m/s²)(2 s)²

Calculating this expression will give us the height of the balcony above the ground.

Calculation of the Velocity of the Ball at Impact

To calculate the velocity of the ball at the moment it hits the ground, we can use the equation for the final velocity of an object in free fall:

v = v₀ + gt

Where: - v is the final velocity - v₀ is the initial velocity - g is the acceleration due to gravity (approximately 9.8 m/s²) - t is the time

Substituting the given values into the equation, we have:

v = 5 m/s + (9.8 m/s²)(2 s)

Calculating this expression will give us the velocity of the ball at the moment it hits the ground.

Calculation Results

Let's calculate the height of the balcony and the velocity of the ball at impact.

Height of the balcony above the ground: Δy = (5 m/s)(2 s) + (1/2)(9.8 m/s²)(2 s)²

Velocity of the ball at impact: v = 5 m/s + (9.8 m/s²)(2 s)

Calculating these expressions will give us the final answers.

Calculation

Height of the balcony above the ground: Δy = (5 m/s)(2 s) + (1/2)(9.8 m/s²)(2 s)² Δy = 10 m + (1/2)(9.8 m/s²)(4 s²) Δy = 10 m + (1/2)(9.8 m/s²)(16 s²) Δy = 10 m + 78.4 m Δy = 88.4 m

Velocity of the ball at impact: v = 5 m/s + (9.8 m/s²)(2 s) v = 5 m/s + (9.8 m/s²)(2 s) v = 5 m/s + 19.6 m/s v = 24.6 m/s

Answer

The height of the balcony above the ground is 88.4 meters and the velocity of the ball at the moment it hits the ground is 24.6 m/s.