Question

Из точки, находящейся на поверхности Земли, выстреливаются по всем направлениям с одинаковыми скоростями тарелочки для стрельбы по мишеням. Наибольшее расстояние, на которое смогли улететь тарелочки 10 м. Найдите максимально высоту полета тарелочек. Сопротивлением воздуха пренебречь. Ответы укажите в метрах, округлив до десятых.

Answer 1

Наиб высота под  H= v₀²sin²α/2g     
Наиб дальн  S=v₀²sin2α/g      при угле 45 град. 
Поделим первое уравнение на второе, получим
H/S=(v₀²sin²α/2g)•(g/v₀²sin2α)=sin²α/(2sin2α)=sin²45⁰/(2sin2•45⁰)=0.5/2•1=0,25.
 H=S•0,25=10•0,25=2,5 м 
Ответ: Нмакс=2,5 м

Answer 2

Problem Analysis

We are given that frisbees are being shot in all directions from a point on the surface of the Earth with the same speed. The maximum distance the frisbees can travel is 10 meters. We need to find the maximum height the frisbees can reach, neglecting air resistance.

Solution

To find the maximum height the frisbees can reach, we can use the concept of projectile motion. In projectile motion, the maximum height is reached when the vertical component of the initial velocity becomes zero.

Let's assume the initial velocity of the frisbees is v m/s. The frisbees will reach their maximum height when the vertical component of the initial velocity becomes zero. At this point, the frisbees will start falling back down due to gravity.

Using the equations of motion, we can find the time it takes for the frisbees to reach their maximum height. The equation for the vertical displacement of an object in projectile motion is given by:

h = (v^2 * sin^2(theta)) / (2 * g)

where: - h is the maximum height - v is the initial velocity - theta is the launch angle (which is 45 degrees in this case, as the frisbees are shot in all directions) - g is the acceleration due to gravity (approximately 9.8 m/s^2)

We are given that the maximum distance the frisbees can travel is 10 meters. Using this information, we can find the initial velocity v using the equation for horizontal displacement:

d = v^2 * sin(2 * theta) / g

where: - d is the maximum distance (10 meters in this case)

Solving this equation for v, we can substitute the value of v into the equation for the maximum height h to find the answer.

Calculation

Let's calculate the maximum height using the given information.

Using the equation for horizontal displacement:

10 = v^2 * sin(2 * 45) / 9.8

Simplifying the equation:

10 = v^2 * sin(90) / 9.8

Since sin(90) = 1, the equation becomes:

10 = v^2 / 9.8

Solving for v:

v^2 = 10 * 9.8

v^2 = 98

v = sqrt(98) ≈ 9.899 m/s

Now, substituting the value of v into the equation for the maximum height:

h = (9.899^2 * sin^2(45)) / (2 * 9.8)

h = (9.899^2 * 0.5^2) / (2 * 9.8)

h ≈ 2.5 meters

Therefore, the maximum height the frisbees can reach is approximately 2.5 meters.

Answer

The maximum height the frisbees can reach is approximately 2.5 meters.