Question

Тело свободно падает без начальной скорости и достигает земли за 4 секунды. за какое время тело упало бы на землю если его бросить с этой же высоты вниз с начальной скоростью 29.4 м/с. И если возможно то сделать как дано: эти числа решение: ответ

Answer 1

• H = (g t²)/2 = 5*16 = 80 м - с такой высоты бросают тело

• H = v0 t' + (g t'²)/2

○ 80 = 29.4 t' + 5 t'²

○ 5 t'² + 29.4 t' - 80 = 0

• t ≈ 2.02 c - за столько тело достигнет земли при начальной скорости 29.4 м/c

Answer 2

Problem Analysis

We are given that an object falls freely without any initial velocity and reaches the ground in 4 seconds. We need to determine the time it would take for the object to fall to the ground if it is thrown downward from the same height with an initial velocity of 29.4 m/s.

Solution

When an object falls freely, its motion can be described using the equations of motion. In this case, we can use the equation for displacement:

s = ut + (1/2)gt^2

where: - s is the displacement (height) of the object, - u is the initial velocity of the object, - t is the time, and - g is the acceleration due to gravity.

Since the object is falling freely, the acceleration due to gravity is approximately 9.8 m/s^2.

Let's calculate the time it takes for the object to fall to the ground when thrown downward with an initial velocity of 29.4 m/s.

Calculation

Given: - Initial velocity (u) = 29.4 m/s - Time taken to reach the ground (t) = 4 s

Using the equation of motion, we can rearrange it to solve for time (t):

s = ut + (1/2)gt^2

Rearranging the equation:

(1/2)gt^2 + ut - s = 0

Substituting the given values:

(1/2)(9.8)(t^2) + (29.4)(t) - s = 0

Since we know that the object reaches the ground in 4 seconds, the displacement (s) can be calculated using the equation:

s = (1/2)gt^2

Substituting the values:

s = (1/2)(9.8)(4^2) = 78.4 m

Now, substituting the values into the equation:

(1/2)(9.8)(t^2) + (29.4)(t) - 78.4 = 0

We can solve this quadratic equation to find the value of t.

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

where: - a = (1/2)(9.8) = 4.9 - b = 29.4 - c = -78.4

Substituting the values:

t = (-29.4 ± √((29.4)^2 - 4(4.9)(-78.4))) / (2(4.9))

Simplifying the equation:

t = (-29.4 ± √(861.36 + 1529.28)) / 9.8

t = (-29.4 ± √(2390.64)) / 9.8

Taking the positive root:

t = (-29.4 + √(2390.64)) / 9.8

Calculating the value:

t ≈ 1.6 s

Therefore, if the object is thrown downward from the same height with an initial velocity of 29.4 m/s, it would take approximately 1.6 seconds to reach the ground.

Answer

If the object is thrown downward from the same height with an initial velocity of 29.4 m/s, it would take approximately 1.6 seconds to reach the ground.