Question

Лыжник скатывается с горы без начальной скорости равноускорено. На середине спуска его скорость 8м/с. Найдите ускорение и его скорость в конце спуска если протяжённость горы 2000 метров. Результат округлите до тысячных. ЗАРАНЕЕ СПАСИБО

Answer 1

S₁ = V²/2a

a = V²/2S₁ = 64 / 2000 = 0.032 м/с²

V = at = 0.032 * 353.5 = 11.312 м/с

t = √2S/a = √2 * 2000 / 0.032 = √125000 ~ 353.5 с

Ответ: 0.032 м/с₂: 11.312 м/с

Answer 2

Calculation of Acceleration and Final Velocity

To find the acceleration and final velocity of the skier at the end of the descent, we can use the equations of motion. Let's denote the initial velocity as v0, the final velocity as v, the acceleration as a, and the distance traveled as s.

Given: - Initial velocity (v0) is 0 m/s (the skier starts with no initial velocity). - Velocity at the midpoint of the descent (v) is 8 m/s. - Distance traveled (s) is 2000 meters.

We can use the following equations of motion:

1. v = v0 + at 2. s = v0t + (1/2)at^2 3. v^2 = v0^2 + 2as

Since the skier starts with no initial velocity (v0 = 0), equation 1 simplifies to v = at.

Let's solve for the acceleration (a) first:

From equation 1, we have v = at. Substituting v = 8 m/s and rearranging the equation, we get:

8 = a * t

We need to find the time (t) it takes for the skier to reach the midpoint of the descent. To do this, we can use equation 2:

s = v0t + (1/2)at^2

Substituting v0 = 0 and s = 2000 m, the equation becomes:

2000 = (1/2)at^2

Now we have two equations:

1. 8 = a * t 2. 2000 = (1/2)at^2

We can solve these equations simultaneously to find the acceleration (a) and the time (t).

Calculation Steps:

1. Rearrange equation 1 to solve for t:

t = 8 / a

2. Substitute the value of t into equation 2:

2000 = (1/2)a(8 / a)^2

3. Simplify equation 2:

2000 = 32 / a

4. Rearrange equation 3 to solve for a:

a = 32 / 2000

5. Calculate the value of a:

a = 0.016 m/s^2

Now that we have the acceleration (a), we can find the final velocity (v) using equation 1:

v = at

Substituting a = 0.016 m/s^2, we get:

v = 0.016 * t

To find the time (t) it takes for the skier to reach the end of the descent, we can use equation 2:

2000 = (1/2)at^2

Substituting a = 0.016 m/s^2, the equation becomes:

2000 = (1/2) * 0.016 * t^2

Simplifying the equation:

2000 = 0.008 * t^2

Rearranging the equation to solve for t:

t^2 = 2000 / 0.008

t^2 = 250000

t = sqrt(250000)

t ≈ 500 seconds

Now we can calculate the final velocity (v) using the value of t:

v = 0.016 * 500

v ≈ 8 m/s

Therefore, the acceleration (a) is approximately 0.016 m/s^2 and the final velocity (v) at the end of the descent is approximately 8 m/s.

Please note that the values have been rounded to the nearest thousandth as requested.