Question

Стальной шарик брошенный с горизонтальной поверхности площадки под углом к горизонту упал на площадку через 1,5 с на расстоянии 15 и от места броска. Найти радиус кривизны траектории в верхней точке траектории.

Answer 1

Ответ:

R=V^2/g=(s/t)^2/g=10м

Объяснение:

Answer 2

Calculation of the Radius of Curvature of the Trajectory

To find the radius of curvature of the trajectory of a steel ball thrown from a horizontal surface at an angle to the horizon, we need to use the given information: the ball falls on the surface after 1.5 seconds at a distance of 15 meters from the point of release.

The radius of curvature of the trajectory can be calculated using the formula:

R = (v^2 * sin(2θ)) / g

Where: - R is the radius of curvature - v is the initial velocity of the ball - θ is the angle of projection - g is the acceleration due to gravity

In this case, we are given the time of flight (1.5 seconds) and the horizontal range (15 meters). We can use these values to calculate the initial velocity and the angle of projection.

Calculation of Initial Velocity

The initial velocity of the ball can be calculated using the formula:

v = R / t

Where: - v is the initial velocity - R is the horizontal range - t is the time of flight

Substituting the given values, we have:

v = 15 / 1.5 = 10 m/s

Calculation of Angle of Projection

The angle of projection can be calculated using the formula:

θ = sin^(-1)((g * t) / (2 * v))

Substituting the given values, we have:

θ = sin^(-1)((9.8 * 1.5) / (2 * 10))

Using a calculator, we find:

θ ≈ 0.75 radians

Calculation of Radius of Curvature

Now that we have the initial velocity (v = 10 m/s) and the angle of projection (θ ≈ 0.75 radians), we can calculate the radius of curvature using the formula mentioned earlier:

R = (v^2 * sin(2θ)) / g

Substituting the values, we have:

R = (10^2 * sin(2 * 0.75)) / 9.8

Using a calculator, we find:

R ≈ 6.12 meters

Therefore, the radius of curvature of the trajectory at the highest point is approximately 6.12 meters.

Please note that the calculations provided are based on the given information and assumptions.