Question

4.С башни выпустили вверх стрелу из лука. Если начальная скорость стрелы равна 30 м/с и t - время полёта стрелы (в секундах), то расстояние h (в метрах) стрелы от поверхности земли можно найти по формуле һ= - 3t²+30t+12. Определите: а) Высоту башни. б) Какой наибольшей высоты достигнет стрела. в)Через сколько секунд стрела будет на высоте 39 м. [3] будте добры помогите с заданием......​

Answer 1

Ответ:

Вершина параболы функции квадратного трехчлена у=a*x^2+b*x+c имеет абсциссу х=-b/(2*a). То есть максимум высоты будет при значении времени, равном -50/(2*(-5))=5 сек. Подставим это значение в формулу получим h=-5*5^2+50*5+20=-125+250+20=145 метров

Answer 2

Task Analysis

To solve this problem, we need to find the height of the tower, the maximum height reached by the arrow, and the time at which the arrow will be at a height of 39 meters. We are given the initial velocity of the arrow (30 m/s) and the formula to calculate the height of the arrow at any given time.

Solution

Let's solve each part of the problem step by step.

# a) Height of the Tower

To find the height of the tower, we can use the formula provided: h = -3t² + 30t + 12. However, we need to know the time at which the arrow hits the ground to find the height of the tower. Since this information is not provided, we cannot determine the height of the tower.

# b) Maximum Height Reached by the Arrow

To find the maximum height reached by the arrow, we can use the formula for the height of the arrow at any given time: h = -3t² + 30t + 12. The maximum height occurs at the vertex of the parabolic function, which is given by the formula t = -b / (2a), where a = -3 and b = 30. Plugging in these values, we can find the time at which the arrow reaches its maximum height. Let's calculate it:

t = -30 / (2 * -3) = 5 seconds

Now, we can substitute this time value back into the formula to find the maximum height:

h = -3(5)² + 30(5) + 12 = 75 meters

Therefore, the arrow reaches a maximum height of 75 meters.

# c) Time at which the Arrow is at a Height of 39 meters

To find the time at which the arrow is at a height of 39 meters, we can set the formula for the height of the arrow equal to 39 and solve for t:

-3t² + 30t + 12 = 39

Simplifying the equation:

-3t² + 30t + 12 - 39 = 0 -3t² + 30t - 27 = 0

Dividing the equation by -3 to simplify further:

t² - 10t + 9 = 0

Now, we can factorize the equation:

(t - 1)(t - 9) = 0

Setting each factor equal to zero and solving for t:

t - 1 = 0 --> t = 1 second t - 9 = 0 --> t = 9 seconds

Therefore, the arrow will be at a height of 39 meters at 1 second and 9 seconds.

Summary

In summary: - The height of the tower cannot be determined without knowing the time at which the arrow hits the ground. - The arrow reaches a maximum height of 75 meters. - The arrow will be at a height of 39 meters at 1 second and 9 seconds.

Please let me know if there's anything else I can help you with!