Question

Дальность полета камня, брошенного под углом к горизонту со скоростью v0, оказалась вдвое меньше максимально возможной при той же начальной скорости. Под каким углом к горизонту брошен камень? Сопротивление воздуха не учитывать. Ответ приведите в градусах.

Answer 1

Vy = V*sin(a)
Vx = V*cos(a)

Рассмотрим движение вдоль оси OY:
0 = Vy * t - g*t^2/2
Отсюда t подъема равно:   t под = 2*Vy/g = 2*V*sin(a)/g
Время полета
t = 2*t под

Дальность полета: S = Vx*t = V*cos(a)*2*2*V*sin(a)/g = 2*V^2*sin(2*a)/g

Максимальная дальность достигается при угле 45 градусов,
тогда sin (2*45)= sin(90) =1
Smax = 2*V^2/g
S = V^2/g
Тогда

2*V^2*sin(2a)/g = V^2/g

sin (2a)=1/2

2a = 30 градусов

Значит, а=15 градусов

Answer 2

Finding the Angle of Projectile

To find the angle at which the stone is thrown, we can use the given information that the maximum possible range of the stone is twice the range achieved when thrown at the same initial velocity. Let's denote the angle at which the stone is thrown as θ.

The range of a projectile launched at an angle θ with an initial velocity v0 can be calculated using the formula:

R = (v0^2 * sin(2θ)) / g,

where R is the range, v0 is the initial velocity, θ is the angle, and g is the acceleration due to gravity.

According to the given information, the maximum possible range is twice the range achieved when thrown at the same initial velocity. Mathematically, this can be expressed as:

2 * R = (v0^2 * sin(2θ)) / g.

Simplifying the equation, we have:

sin(2θ) = 2 * (R * g) / v0^2.

Now, we need to find the angle θ. To do that, we can take the inverse sine (also known as arcsine) of both sides of the equation:

2θ = arcsin(2 * (R * g) / v0^2).

Finally, we can solve for θ by dividing both sides of the equation by 2:

θ = (1/2) * arcsin(2 * (R * g) / v0^2).

Please note that the given problem statement does not provide specific values for the initial velocity v0 or the range R. Therefore, we cannot provide a numerical answer without these values.

If you have the specific values for v0 and R, you can substitute them into the equation above to find the angle θ.