Question

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

Answer 1

То есть нужно найти координаты х и у, так как тело движется по параболе.
х=V₀cosαt, х=10*cos30° *0,5 ≈ 4,33 м
у=V₀sinαt -gt²/2, у=10* sin30° *0,5 -10*0,5²/2=2,5-1,25=1,25 м
Ответ: в точке ( 4,33 м; 1,25 м)

Answer 2

Problem Analysis

We are given that an object is thrown with a speed of 10 m/s at an angle of 30 degrees to the horizontal. We need to determine the object's position after 0.5 seconds.

Solution

To solve this problem, we can break down the initial velocity into its horizontal and vertical components.

The horizontal component of the velocity (v_x) remains constant throughout the motion and is given by:

v_x = v * cos(theta)

where v is the initial speed (10 m/s) and theta is the angle (30 degrees).

The vertical component of the velocity (v_y) changes due to the acceleration due to gravity. The acceleration due to gravity is approximately 9.8 m/s^2. The vertical component of the velocity at any time t is given by:

v_y = v * sin(theta) - g * t

where g is the acceleration due to gravity (9.8 m/s^2) and t is the time (0.5 seconds).

To find the object's position after 0.5 seconds, we need to determine the horizontal and vertical displacements. The horizontal displacement (x) is given by:

x = v_x * t

where t is the time (0.5 seconds) and v_x is the horizontal component of the velocity.

The vertical displacement (y) is given by:

y = v_y * t - (1/2) * g * t^2

where t is the time (0.5 seconds), v_y is the vertical component of the velocity, and g is the acceleration due to gravity.

Let's calculate the horizontal and vertical displacements and determine the object's position after 0.5 seconds.

Calculation

Given: - Initial speed (v) = 10 m/s - Angle (theta) = 30 degrees - Time (t) = 0.5 seconds - Acceleration due to gravity (g) = 9.8 m/s^2

Using the equations mentioned above, we can calculate the horizontal and vertical displacements:

Horizontal component of velocity (v_x): v_x = v * cos(theta) = 10 * cos(30) = 10 * 0.866 = 8.66 m/s

Vertical component of velocity (v_y): v_y = v * sin(theta) - g * t = 10 * sin(30) - 9.8 * 0.5 = 10 * 0.5 - 9.8 * 0.5 = 5 - 4.9 = 0.1 m/s

Horizontal displacement (x): x = v_x * t = 8.66 * 0.5 = 4.33 m

Vertical displacement (y): y = v_y * t - (1/2) * g * t^2 = 0.1 * 0.5 - 0.5 * 9.8 * 0.5^2 = 0.05 - 0.5 * 9.8 * 0.25 = 0.05 - 1.225 = -1.175 m

The negative sign indicates that the object is below the initial position.

Answer

The object will be at a horizontal displacement of 4.33 meters and a vertical displacement of -1.175 meters after 0.5 seconds.