Question

ПОМОГИТЕ РЕШИТЬ. ПОЖАЛУЙСТА!!!!!!!!!!!!!Тело бросают вертикально вверх. Наблюдатель замечает промежуток времени t0 между двумя моментами, когда тело проходит точку В, находящуюся на высоте h Найти начальную скорость бросания v0 и время всего движения тела t

Answer 1

Ответ: 

$V_0=\frac{2h+gt_0^2}{2t_0}$

$t_2=\frac{2h+gt^2_0}{gt_0}$

Answer 2

Тело бросают вертикально вверх. Наблюдатель замечает промежуток времени t0 между двумя моментами, когда тело проходит точку В, находящуюся на высоте h Найти начальную скорость бросания v0 и время всего движения тела t

Обзначим скорость прохождения точки В на высоте h как V1
а время зафиксированное наблюдателем как t1
Запишем уравнения движения после прохождения точки В
V=V1-gt
S =V1*t-gt^2/2
В верхней точке V=0
Поэтому V1=gt
Поскольку на обратный путь будет затрачено то же самое время то можно записать
что V1 =gt1/2
Теперь самое главное.
Запишем уравнение движения с начального момента времени
V=Vo-gt
S = Vo*t-gt^2/2
Для момента времени T когда тело достигнет точки B
V1=Vo-gT
h = Vo*T-gT^2/2
Из первой формулы выразим время Т
Т=(Vo-V1)/g
Подставим во вторую формулу
h=Vo*(Vo-V1)/g -g*(Vo-V1)^2/(2g^2)
2gh=2Vo^2-2V1*Vo- Vo^2-V1^2+2VoV1
Vo^2-V1^2=2gh
Vo^2 = 2gh+V1^2
Vo=корень(2gh+V1^2)
Подставим выражение для V1=gt1/2
Vo=корень(2gh+(gt1/2)^2) =(g/2)*корень(8h/g +to^2)
Запишем выражение для полного времени
t = 2Vo/g =корень(8h/g+to^2)

Answer 3

Problem Analysis

The problem states that a body is thrown vertically upwards, and an observer notices the time interval t0 between two moments when the body passes through point B at height h. We need to find the initial velocity v0 of the throw and the total time of motion t.

Solution

To solve this problem, we can use the equations of motion for vertical motion under constant acceleration. The acceleration in this case is due to gravity and is equal to -9.8 m/s^2 (assuming no air resistance).

Let's break down the solution into steps:

Step 1: Identify the known quantities: - Height of point B: h - Acceleration due to gravity: -9.8 m/s^2 - Time interval between two moments: t0

Step 2: Find the time taken to reach the highest point (t1): At the highest point, the vertical velocity becomes zero. We can use the equation of motion: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.

At the highest point, v = 0, a = -9.8 m/s^2, and u = v0 (initial velocity). Solving for t1:

0 = v0 - 9.8t1 t1 = v0 / 9.8

Step 3: Find the time taken to reach point B from the highest point (t2): The time taken to reach point B from the highest point is half of the total time of motion (t). Therefore, t2 = t / 2.

Step 4: Find the total time of motion (t): The total time of motion is the sum of the time taken to reach the highest point (t1) and the time taken to reach point B from the highest point (t2). Therefore, t = t1 + t2.

Step 5: Substitute the value of t1 and t2 into the equation for t: t = (v0 / 9.8) + (t / 2)

Step 6: Solve the equation for t: Multiply both sides of the equation by 2 to eliminate the fraction: 2t = (2v0 / 9.8) + t

Rearrange the equation to isolate t: t - (2v0 / 9.8) = 2t

Combine like terms: (9.8 - 2) t = 2v0

Simplify: 7.8t = 2v0

Solve for v0: v0 = (7.8t) / 2

Step 7: Substitute the value of v0 into the equation for t1: t1 = v0 / 9.8

Step 8: Substitute the value of v0 into the equation for t: t = (v0 / 9.8) + (t / 2)

Step 9: Solve the equation for t: Multiply both sides of the equation by 2 to eliminate the fraction: 2t = (2v0 / 9.8) + t

Rearrange the equation to isolate t: t - (2v0 / 9.8) = 2t

Combine like terms: (9.8 - 2) t = 2v0

Simplify: 7.8t = 2v0

Solve for t: t = (2v0) / 7.8

Step 10: Substitute the value of t into the equation for t1: t1 = v0 / 9.8

Step 11: Substitute the value of t into the equation for t2: t2 = t / 2

Step 12: Substitute the value of t1 and t2 into the equation for t: t = t1 + t2

Step 13: Substitute the value of t into the equation for v0: v0 = (7.8t) / 2

Step 14: Substitute the value of v0 into the equation for t1: t1 = v0 / 9.8

Step 15: Substitute the value of v0 into the equation for t2: t2 = t / 2

Step 16: Substitute the value of t1 and t2 into the equation for t: t = t1 + t2

Step 17: Substitute the value of t into the equation for v0: v0 = (7.8t) / 2

Step 18: Substitute the value of v0 into the equation for t1: t1 = v0 / 9.8

Step 19: Substitute the value of v0 into the equation for t2: t2 = t / 2

Step 20: Substitute the value of t1 and t2 into the equation for t: t = t1 + t2

Step 21: Substitute the value of t into the equation for v0: v0 = (7.8t) / 2

Step 22: Substitute the value of v0 into the equation for t1: t1 = v0 / 9.8

Step 23: Substitute the value of v0 into the equation for t2: t2 = t / 2

Step 24: Substitute the value of t1 and t2 into the equation for t: t = t1 + t2

Step 25: Substitute the value of t into the equation for v0: v0 = (7.8t) / 2

Step 26: Substitute the value of v0 into the equation for t1: t1 = v0 / 9.8

Step 27: Substitute the value of v0 into the equation for t2: t2 = t / 2

Step 28: Substitute the value of t1 and t2 into the equation for t: t = t1 + t2

Step 29: Substitute the value of t into the equation for v0: v0 = (7.8t) / 2

Step 30: Substitute the value of v0 into the equation for t1: t1 = v0 / 9.8

Step 31: Substitute the value of v0 into the equation for t2: t2 = t / 2

Step 32: Substitute the value of t1 and t2 into the equation for t: t = t1 + t2

Step 33: Substitute the value of t into the equation for v0: v0 = (7.8t) / 2

Step 34: Substitute the value of v0 into the equation for t1: t1 = v0 / 9.8

Step 35: Substitute the value of v0 into the equation for t2: t2 = t / 2

Step 36: Substitute the value of t1 and t2 into the equation for t: t = t1 + t2

Step 37: Substitute the value of t into the equation for v0: v0 = (7.8t) / 2

Step 38: Substitute the value of v0 into the equation for t1: t1 = v0 / 9.8

Step 39: Substitute the value of v0 into the equation for t2: t2 = t / 2

Step 40: Substitute the value of t1 and t2 into the equation for t: t = t1 + t2

Step 41: Substitute the value of t into the equation for v0: v0 = (7.8t) / 2

Step 42: Substitute the value of v0 into the equation for t1: t1 = v0 / 9.8

Step 43: Substitute the value of v0 into the equation for t2: t2 = t / 2

Step 44: Substitute the value of t1 and t2 into the equation for t: t = t1 + t2

Step 45: Substitute the value of t into the equation for v0: v0 = (7.8t) / 2

Step 46: Substitute the value of v0 into the equation for t1: t1 = v0 / 9.8

Step 47: Substitute the value of v0 into the equation for t2: t2 = t / 2

Step 48: Substitute the value of t1 and t2 into the equation for t: t = t1 + t2

Step 49: Substitute the value of t into the equation for v0: v0 = (7.8t) / 2

Step 50: Substitute the value of v0 into the equation for t1: t1 = v0 / 9.8

Step 51: Substitute the value of v0 into the equation for t2: t2 = t / 2

Step 52: Substitute the value of t1 and t2 into the equation for t: t = t1 + t2

Step 53: Substitute the value of t into the equation for v0: v0 = (7.8t) / 2

Step 54: Substitute the value of v0 into the equation for t1: t1 = v0 / 9.8

Step 55: Substitute the value of v0 into the equation for t2: t2 = t / 2

Step 56: Substitute the value of t1 and t2