Question

Тело брошено со скоростью 10 м/с под углом 30 градусов к горизонту. Где оно будет через 0,5с.

Answer 1

X=V0*cosa*t=10*0,866*0,5=4,33 м
y=(V0*s0na)*t -5*t^2=10*0,5*0,5-5*0,5^2=1,25 м
Перемещение относительно точки бросания S=sqrt(x^2+y^2)=sqrt(1,25^2+4,33^2)=4,5 м

Answer 2

Calculation of the Horizontal and Vertical Components of Velocity

To determine the position of the body after 0.5 seconds, we need to calculate the horizontal and vertical components of its velocity.

The initial velocity of the body is given as 10 m/s at an angle of 30 degrees to the horizontal.

Using trigonometry, we can calculate the horizontal and vertical components of the velocity.

The horizontal component of velocity (Vx) can be calculated using the formula:

Vx = V * cos(θ)

where V is the initial velocity and θ is the angle of projection.

Substituting the given values:

Vx = 10 m/s * cos(30 degrees)

To calculate the vertical component of velocity (Vy), we can use the formula:

Vy = V * sin(θ)

Substituting the given values:

Vy = 10 m/s * sin(30 degrees)

Let's calculate these values:

Vx = 10 m/s * cos(30 degrees) = 8.66 m/s.

Vy = 10 m/s * sin(30 degrees) = 5 m/s.

Calculation of the Horizontal and Vertical Displacements

Now that we have the horizontal and vertical components of velocity, we can calculate the horizontal and vertical displacements after 0.5 seconds.

The horizontal displacement (dx) can be calculated using the formula:

dx = Vx * t

where Vx is the horizontal component of velocity and t is the time.

Substituting the given values:

dx = 8.66 m/s * 0.5 s

The vertical displacement (dy) can be calculated using the formula:

dy = Vy * t + (1/2) * g * t^2

where Vy is the vertical component of velocity, t is the time, and g is the acceleration due to gravity.

Substituting the given values:

dy = 5 m/s * 0.5 s + (1/2) * 9.8 m/s^2 * (0.5 s)^2

Let's calculate these values:

dx = 8.66 m/s * 0.5 s = 4.33 m.

dy = 5 m/s * 0.5 s + (1/2) * 9.8 m/s^2 * (0.5 s)^2 = 1.225 m.

Calculation of the Final Position

To determine the final position of the body after 0.5 seconds, we need to combine the horizontal and vertical displacements.

The final position can be calculated using the formulas:

x = dx y = dy

Substituting the calculated values:

x = 4.33 m y = 1.225 m

Therefore, the body will be at the position (4.33 m, 1.225 m) after 0.5 seconds.

Please note that these calculations assume no air resistance and a constant acceleration due to gravity.