Question

Снаряд вылетает под углом 60 градусов горизонту с начальной скоростью V0=500 м/с. найти время, дальность полёта снаряда, а также максимальную высоту его подъёма.

Answer 1

T=2*V0*sina/g=2*500*0,87/10=87 c
L=V0*cosa*t=500*0,5*87=21750 м
H=V0^2*sin^2a/2*g=250000*0,76/2*10=9500 м

Answer 2

Problem Analysis

We are given the initial launch angle of a projectile, which is 60 degrees to the horizontal, and the initial velocity of the projectile, which is 500 m/s. We need to find the time of flight, the range of the projectile, and the maximum height reached by the projectile.

Time of Flight

The time of flight can be calculated using the formula: time of flight = (2 * initial velocity * sin(angle)) / acceleration due to gravity.

Range of the Projectile

The range of the projectile can be calculated using the formula: range = (initial velocity^2 * sin(2 * angle)) / acceleration due to gravity.

Maximum Height

The maximum height reached by the projectile can be calculated using the formula: maximum height = (initial velocity^2 * sin^2(angle)) / (2 * acceleration due to gravity).

Calculation

Let's calculate the time of flight, range, and maximum height of the projectile.

Using the given values: - Initial velocity (V0) = 500 m/s - Launch angle = 60 degrees

We can use the formulae mentioned above to calculate the required values.

Time of Flight

Substituting the values into the formula: time of flight = (2 * 500 * sin(60)) / 9.8

Range of the Projectile

Substituting the values into the formula: range = (500^2 * sin(2 * 60)) / 9.8

Maximum Height

Substituting the values into the formula: maximum height = (500^2 * sin^2(60)) / (2 * 9.8)

Let's calculate the values.

Calculation Results

- Time of flight: 5.10 seconds - Range of the projectile: 1275.51 meters - Maximum height: 318.88 meters

Therefore, the time of flight of the projectile is 5.10 seconds, the range of the projectile is 1275.51 meters, and the maximum height reached by the projectile is 318.88 meters.

Please note that these calculations assume no air resistance and a constant acceleration due to gravity of 9.8 m/s^2.