Question

30 баллов!!! Ракета была выпущена в воздух. Расстояние Н ракеты от земли в момент времени t можно рассчитать по формуле H(t)=80t-5t² а) В какой точке ракета достигнет максимального расстояния от земли? б) Каким будет максимальное расстояние от земли? в) Через какое время ракета приземлится?

Answer 1

Ответ:

Пошаговое объяснение:

S(t)=v0t+gt^2/2

H(t)=80t-5t²

V0= 80

g=10

__________

1) t=v0/g=8s

2) Hmax=v0^2/2g= 320 m

3) T =2t = 16 s

можно еше решить H(t)=0 t'= 0 ; 16

Answer 2

Problem Analysis

We are given the equation for the height of a rocket as a function of time: H(t) = 80t - 5t^2. We need to find the point at which the rocket reaches its maximum distance from the ground, the maximum distance itself, and the time it takes for the rocket to land.

Solution

a) To find the point at which the rocket reaches its maximum distance from the ground, we need to find the vertex of the parabolic function H(t) = 80t - 5t^2. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a = -5 and b = 80. Plugging in these values, we get:

x = -80 / (2 * -5) = 8

To find the y-coordinate of the vertex, we substitute x = 8 into the equation H(t):

H(8) = 80 * 8 - 5 * 8^2 = 640 - 320 = 320

Therefore, the rocket reaches its maximum distance from the ground at the point (8, 320).

b) To find the maximum distance from the ground, we can simply substitute the x-coordinate of the vertex (8) into the equation H(t):

H(8) = 320

Therefore, the maximum distance from the ground is 320 units.

c) To find the time it takes for the rocket to land, we need to find the value of t when H(t) = 0. We can set the equation H(t) = 0 and solve for t:

80t - 5t^2 = 0

Factoring out t, we get:

t(80 - 5t) = 0

This equation is satisfied when t = 0 or 80 - 5t = 0. Solving the second equation for t, we get:

80 - 5t = 0 5t = 80 t = 16

Therefore, the rocket will land after 16 units of time.

Summary

a) The rocket reaches its maximum distance from the ground at the point (8, 320). b) The maximum distance from the ground is 320 units. c) The rocket will land after 16 units of time.